Answer
a. $\begin{bmatrix} -1 & 0 \\ 0 & 1 \end{bmatrix}$
b. $\begin{bmatrix} 1 & 0 & -1 \\ 0 & 1 & -1\end{bmatrix}$
Work Step by Step
a. Using the formula for evaluating matrix products, we have
$\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix} \begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix}=\begin{bmatrix} 1(-1)+0(0) & 1(0)+0(-1) \\ 0(-1)+(-1)(0) & 0(0)+(-1)(-1) \end{bmatrix}=\begin{bmatrix} -1 & 0 \\ 0 & 1 \end{bmatrix}$
b. Similarly, we have
$\begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix} \begin{bmatrix} -1 & 0 & 1 \\ 0 & -1 &1 \end{bmatrix}=\begin{bmatrix} 1+0 & 0+0 & -1+0 \\ 0+0 & 0+1 & 0-1 \end{bmatrix}=\begin{bmatrix} 1 & 0 & -1 \\ 0 & 1 & -1\end{bmatrix}$
