Answer
\begin{align*} AB&= \left[\begin{array}{rrr}{-21} & {0} & {0} \\ {0} & {-20} & {0} \\ {0} & {0} & {0}\end{array}\right] . \end{align*} \begin{align*} BA&= \left[\begin{array}{rrr}{-21} & {0} & {0} \\ {0} & {-20} & {0} \\ {0} & {0} & {0}\end{array}\right] . \end{align*}
Work Step by Step
Given $$ A=\left[\begin{array}{rrr}{3} & {0} & {0} \\ {0} & {-5} & {0} \\ {0} & {0} & {0}\end{array}\right], \quad B=\left[\begin{array}{rrr}{-7} & {0} & {0} \\ {0} & {4} & {0} \\ {0} & {0} & {12}\end{array}\right] $$ We have \begin{align*} AB&= \left[\begin{array}{rrr}{3} & {0} & {0} \\ {0} & {-5} & {0} \\ {0} & {0} & {0}\end{array}\right]\left[\begin{array}{rrr}{-7} & {0} & {0} \\ {0} & {4} & {0} \\ {0} & {0} & {12}\end{array}\right]\\ &=\left[\begin{array}{rrr}{-21} & {0} & {0} \\ {0} & {-20} & {0} \\ {0} & {0} & {0}\end{array}\right] . \end{align*} \begin{align*} BA&= \left[\begin{array}{rrr}{-7} & {0} & {0} \\ {0} & {4} & {0} \\ {0} & {0} & {12}\end{array}\right]\left[\begin{array}{rrr}{3} & {0} & {0} \\ {0} & {-5} & {0} \\ {0} & {0} & {0}\end{array}\right]\\ &=\left[\begin{array}{rrr}{-21} & {0} & {0} \\ {0} & {-20} & {0} \\ {0} & {0} & {0}\end{array}\right] . \end{align*}
