There `n`

variables **x1,x2,...,xn** represented as **X**, `n`

equations whose coefficient matrix (n*n) is represented as **A**, and this system looks like this:

**AX = B (mod k)**

Initially I was trying to solve this system using ordinary **Gaussian Elimination**, can't seem to get right solution.

Can't I just apply ordinary **Gaussian Elimination** here on system of congruence? What is the right way to solve it?

Any suggestion is highly appreciated.