Answer
$$AB=\left[\begin{array}{rrr}{-10} & {0} \\ {0} & {-12} \end{array}\right] .$$
$$BA=\left[\begin{array}{rrr}{-10} & {0} \\ {0} & {-12} \end{array}\right] .$$
Work Step by Step
Given
$$
A=\left[\begin{array}{rr}{2} & {0} \\ {0} & {-3}\end{array}\right], \quad B=\left[\begin{array}{rr}{-5} & {0} \\ {0} & {4}\end{array}\right]
$$
We have
\begin{align*}
AB&= \left[\begin{array}{rr}{2} & {0} \\ {0} & {-3}\end{array}\right]\left[\begin{array}{rr}{-5} & {0} \\ {0} & {4}\end{array}\right]\\
&=\left[\begin{array}{rrr}{-10} & {0} \\ {0} & {-12} \end{array}\right]
.
\end{align*}
\begin{align*}
BA&= \left[\begin{array}{rr}{-5} & {0} \\ {0} & {4}\end{array}\right]\left[\begin{array}{rr}{2} & {0} \\ {0} & {-3}\end{array}\right]\\
&=\left[\begin{array}{rrr}{-10} & {0} \\ {0} & {-12} \end{array}\right]
.
\end{align*}
