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) $AB=\prod$
(b) $BA=$
(c) $B^2=$

Step 1 ：$AB=\left[\begin{array}{ccc}2& 0-3& 3\end{array}\right]\left[\begin{array}{ccc}-1& -30& 2\end{array}\right]$

Step 2 ：$AB=\left[\begin{array}{ccc}(2\ast -1+0\ast 0)& (2\ast -3+0\ast 2)(-3\ast -1+3\ast 0)& (-3\ast -3+3\ast 2)\end{array}\right]$

Step 3 ：$AB=\left[\begin{array}{ccc}-2& -63& 9\end{array}\right]$

Step 4 ：$BA=\left[\begin{array}{ccc}-1& -30& 2\end{array}\right]\left[\begin{array}{ccc}2& 0-3& 3\end{array}\right]$

Step 5 ：$BA=\left[\begin{array}{ccc}(-1\ast 2+-3\ast -3)& (-1\ast 0+-3\ast 3)(0\ast 2+2\ast -3)& (0\ast 0+2\ast 3)\end{array}\right]$

Step 6 ：$BA=\left[\begin{array}{ccc}7& -9-6& 6\end{array}\right]$

Step 7 ：$B^2=\left[\begin{array}{ccc}-1& -30& 2\end{array}\right]\left[\begin{array}{ccc}-1& -30& 2\end{array}\right]$

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

Step 9 ：$B^2=\left[\begin{array}{ccc}1& -90& 4\end{array}\right]$

Step 10 ：$\boxed{{\displaystyle AB=\left[\begin{array}{ccc}-2& -63& 9\end{array}\right],BA=\left[\begin{array}{ccc}7& -9-6& 6\end{array}\right],B^2=\left[\begin{array}{ccc}1& -90& 4\end{array}\right]}}$