give an example of two matrices a and b for which ab=0 but ba is not equal to 0 where 0 is null matrix and a and b are both non zero matrices

let A and B be two matrices of order 2*2 such that A and B both are not null matrix.

$let A=\left[\begin{array}{cc}-1& 1\\ 0& 0\end{array}\right] and B=\left[\begin{array}{cc}1& 1\\ 1& 1\end{array}\right]$

then $AB=\left[\begin{array}{cc}-1+1& -1+1\\ 0& 0\end{array}\right]=\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]$ i.e. AB is a null matrix

and $BA=\left[\begin{array}{cc}1& 1\\ 1& 1\end{array}\right]\left[\begin{array}{cc}-1& 1\\ 0& 0\end{array}\right]=\left[\begin{array}{cc}-1& 1\\ -1& 1\end{array}\right]$ which is not a null matrix.

hope this helps you