Matrix addition, subtraction and multiplication, Bash

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#!/bin/bash
# GNU bash, version 4.4.20

n=2
x=(1 2 3 4)
y=(5 6 7 8)
z=(0 0 0 0)
read ch
case $ch in
1)
        for((i=0;i<n;i++))
        do
           for((j=0;j<n;j++))
            do
                z[$(($n*$i+$j))]=$(( ${x[$(($n*$i+$j))]} + ${y[$(($n*$i+$j))]} ))
            done
        done
        echo "The new matrix after addition is"
        echo ${z[*]}
    ;;
2)
        for((i=0;i<n;i++))
        do
           for((j=0;j<n;j++))
            do
                z[$(($n*$i+$j))]=$(( ${y[$(($n*$i+$j))]} - ${x[$(($n*$i+$j))]} ))
            done
        done
        echo "The new matrix after subtraction is"
        echo ${z[*]}
    ;;
3)
        for((i=0;i<n;i++))
        do
           for((j=0;j<n;j++))
            do
                prod[$(($n*$i+$j))]=0
                for((k=0;k<n;k++))
                do
                    prod[$(( $n*$i+$j ))]=$(( ${prod[$(( $n*$i+$j ))]} + $(( ${x[$(( $n*$i+$k ))]} * ${y[$(( $n*$k+$j ))]} )) ))
                done
            done
        done
        echo "The new matrix after multiplication is"
        echo ${prod[*]}
    ;;

*) echo " exit to quit" 
	;;
esac

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