Square Integer Matrix, C#

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//Rextester.Program.Main is the entry point for your code. Don't change it.
//Compiler version 4.0.30319.17929 for Microsoft (R) .NET Framework 4.5

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text.RegularExpressions;
using System.Text;

namespace Rextester
{
    public class Program
    {
        
        public class SquareIntegerMatrix
        {
            private int[,] InternalRep = null;

public int Rows = 0;
            public int Columns = 0;
            private List<int> Vector = null;
            private void Zero()
            {
                for (int i = 0; i < Rows; i++)
                {
                    for (int j = 0; j < Columns; j++)
                    {
                        InternalRep[i, j] = 0;
                    }
                }
            
            }

private int SignOfElement(int i, int j)
            {
                if ((i + j) % 2 == 0)
                {
                    return 1;
                }
                else
                {
                    return -1;
                }
            }
            //this method determines the sub matrix corresponding to a given element
            private int[,] CreateSmallerMatrix(int[,] input, int i, int j)
            {
                int order = int.Parse(System.Math.Sqrt(input.Length).ToString());
                int[,] output = new int[order - 1, order - 1];
                int x = 0, y = 0;
                for (int m = 0; m < order; m++, x++)
                {
                    if (m != i)
                    {
                        y = 0;
                        for (int n = 0; n < order; n++)
                        {
                            if (n != j)
                            {
                                output[x, y] = input[m, n];
                                y++;
                            }
                        }
                    }
                    else
                    {
                        x--;
                    }
                }
                return output;
            }

public int Determinant()
            {
                return Determinant(this.InternalRep);
            }

private int Determinant(int[,] input)
            {
                int order = int.Parse(System.Math.Sqrt(input.Length).ToString());
                if (order > 2)
                {
                    int value = 0;
                    for (int j = 0; j < order; j++)
                    {
                        int[,] Temp = CreateSmallerMatrix(input, 0, j);
                        value = value + input[0, j] * (SignOfElement(0, j) * Determinant(Temp));
                    }
                    return value;
                }
                else if (order == 2)
                {
                    return ((input[0, 0] * input[1, 1]) - (input[1, 0] * input[0, 1]));
                }
                else
                {
                    return (input[0, 0]);
                }
            }
            
            private void FromVector()
            {
                int cnt = 0;
                for (int i = 0; i < Rows; i++)
                {
                    for (int j = 0; j < Columns; j++)
                    {
                        InternalRep[i, j] = Vector[cnt++];
                    }
                }
            }

public SquareIntegerMatrix(int rows, int columns)
            {
                if (rows != columns)
                {
                    throw new Exception("rows and columns must be equal for square matrix");
                    
                }

this.Rows = rows;
                this.Columns = columns;
                InternalRep = new int[this.Rows, this.Columns];

Zero();
            }

public SquareIntegerMatrix(int[,] RC)
            {
                int rows = RC.GetLength(0);
                int columns = RC.GetLength(1);

if (rows != columns)
                {
                    throw new Exception("rows and columns must be equal for square matrix");

}

this.Rows = rows;
                this.Columns = columns;
                InternalRep = RC;        
            }
            
            public SquareIntegerMatrix(int rows, int columns, List<int> V)
            {
                if (rows != columns)
                {
                    throw new Exception("rows and columns must be equal for square matrix");

}
                
                if (V.Count % rows != 0)
                {
                    throw new Exception("Vector does not contain even row count");
                }

Vector = V;

this.Rows = rows;
                this.Columns = columns;
                InternalRep = new int[this.Rows, this.Columns];

FromVector();
            }

public static SquareIntegerMatrix operator +(SquareIntegerMatrix a, SquareIntegerMatrix b)
            {
                SquareIntegerMatrix ret = new SquareIntegerMatrix(a.Rows, a.Columns);

for (int i = 0; i < ret.Rows; i++)
                {
                    for (int j = 0; j < ret.Columns; j++)
                    {

ret.InternalRep[i, j] = a.InternalRep[i, j] + b.InternalRep[i, j];                        
                    
                    }

}

return ret;
            }
            
            public static SquareIntegerMatrix operator *(SquareIntegerMatrix a, SquareIntegerMatrix b)
            {
                SquareIntegerMatrix ret = new SquareIntegerMatrix(a.Rows, a.Columns);

for (int i = 0; i < ret.Rows; i++)
                {
                    for (int j = 0; j < ret.Columns; j++)
                    {

for (int k = 0; k < ret.Columns; k++)
                        {
                            ret.InternalRep[i, j] += a.InternalRep[i, k] * b.InternalRep[k, j];
                        }
                    
                    }

}

return ret;
            }

public int this[int r, int c]
            {
                get
                {
                    if (!(r < Rows && c < Columns))
                    {
                        throw new Exception("rows and columns out of range of square matrix");
                    }
                    return (InternalRep[r, c]); 
                }
                set { InternalRep[r, c] = value; }
            }

public override string ToString()
            {
                StringBuilder sb = new StringBuilder();
                for (int i = 0; i < Rows; i++)
                {
                    for (int j = 0; j < Columns; j++)
                    {
                        sb.AppendFormat("{0}\t", InternalRep[i, j]);
                    }

sb.Append("\r\n");

}

return sb.ToString();
            }
        }
        
        public static void Main(string[] args)
        {
            List<int> v = new List<int> { 1, 2, 3, 4 };
            List<int> v2= new List<int> { 7, 8, 9, 10 };

SquareIntegerMatrix m = new SquareIntegerMatrix(2, 2, v);
            SquareIntegerMatrix m2 = new SquareIntegerMatrix(2, 2, v2);

SquareIntegerMatrix mm = m * m2;

Console.WriteLine(mm.ToString());
            Console.WriteLine(mm[0, 0]);

mm[0, 0] = 97;
            Console.WriteLine(mm.ToString());
            
            int[,] ir = new int[2, 2];
            
            ir[0, 0] = 1;
            ir[0, 1] = 2;
            ir[1,0] = 3;
            ir[1,1] = 4;
            
            SquareIntegerMatrix mmir = new SquareIntegerMatrix(ir);
            Console.WriteLine(mmir.ToString());
            
            SquareIntegerMatrix mma = m + m2;
            Console.WriteLine(mma.ToString());
            
            
            int[,] mat = 
            {
                {2, 6, 6, 2},
                {2, 7, 3, 6},
                {1, 5, 0, 1},
                {3, 7, 0, 7}            
            };

SquareIntegerMatrix md = new SquareIntegerMatrix(mat);
            Console.WriteLine(md.ToString());
            Console.Write(md.Determinant());
            Console.WriteLine();
            
            
        }
    }
}

Show compiler warnings [ + ] Show input
Compilation time: 0,16 sec, absolute running time: 0,09 sec, cpu time: 0,08 sec, average memory usage: 14 Mb, average nr of threads: 3