Answer
sample answer:
A= $\left[\begin{array}{ll}
1 & 0\\
0 & 1
\end{array}\right]$, B= $\left[\begin{array}{ll}
1 & 2\\
3 & 4
\end{array}\right]$
Work Step by Step
For both products to be defined,
the number of columns in A must equal the number of rows in B,
and the number of columns in B must equal the number of rows in A.
So, take A and B to be 2$\times$2 matrices.
Let one of them be A= $\left[\begin{array}{ll}
1 & 0\\
0 & 1
\end{array}\right]$,
and the other any 2$\times$2 matrix, say, B= $\left[\begin{array}{ll}
1 & 2\\
3 & 4
\end{array}\right]$
Then
AB=$\left[\begin{array}{ll}
1 & 0\\
0 & 1
\end{array}\right]\left[\begin{array}{ll}
1 & 2\\
3 & 4
\end{array}\right]$=$\left[\begin{array}{ll}
1 & 2\\
3 & 4
\end{array}\right]$
and
BA=$\left[\begin{array}{ll}
1 & 2\\
3 & 4
\end{array}\right]\left[\begin{array}{ll}
1 & 0\\
0 & 1
\end{array}\right]$=$\left[\begin{array}{ll}
1 & 2\\
3 & 4
\end{array}\right]$
