Let $A=\left[\begin{array}{cc}2 & 0 \\ -3 & 3\end{array}\right]$ and $B=\left[\begin{array}{cc}-1 & -3 \\ 0 & 2\end{array}\right]$.
Find each matrix below. If a matrix is not defined, click on "Undefined"
(a) $A B=\prod$
(b) $B A=$
(c) $B^{2}=$

Step 1 ：\(A B=\left[\begin{array}{cc}2 & 0 \ -3 & 3\end{array}\right] \left[\begin{array}{cc}-1 & -3 \ 0 & 2\end{array}\right]\)

Step 2 ：\(A B=\left[\begin{array}{cc}(2*-1+0*0) & (2*-3+0*2) \ (-3*-1+3*0) & (-3*-3+3*2)\end{array}\right]\)

Step 3 ：\(A B=\left[\begin{array}{cc}-2 & -6 \ 3 & 9\end{array}\right]\)

Step 4 ：\(B A=\left[\begin{array}{cc}-1 & -3 \ 0 & 2\end{array}\right] \left[\begin{array}{cc}2 & 0 \ -3 & 3\end{array}\right]\)

Step 5 ：\(B A=\left[\begin{array}{cc}(-1*2+-3*-3) & (-1*0+-3*3) \ (0*2+2*-3) & (0*0+2*3)\end{array}\right]\)

Step 6 ：\(B A=\left[\begin{array}{cc}7 & -9 \ -6 & 6\end{array}\right]\)

Step 7 ：\(B^{2}=\left[\begin{array}{cc}-1 & -3 \ 0 & 2\end{array}\right] \left[\begin{array}{cc}-1 & -3 \ 0 & 2\end{array}\right]\)

Step 8 ：\(B^{2}=\left[\begin{array}{cc}(-1*-1+-3*0) & (-1*-3+-3*2) \ (0*-1+2*0) & (0*-3+2*2)\end{array}\right]\)

Step 9 ：\(B^{2}=\left[\begin{array}{cc}1 & -9 \ 0 & 4\end{array}\right]\)

Step 10 ：\(\boxed{A B=\left[\begin{array}{cc}-2 & -6 \ 3 & 9\end{array}\right], B A=\left[\begin{array}{cc}7 & -9 \ -6 & 6\end{array}\right], B^{2}=\left[\begin{array}{cc}1 & -9 \ 0 & 4\end{array}\right]}\)