If $A =\begin{bmatrix}1&0\\0&-1\end{bmatrix}$ and $B =\begin{bmatrix}0&1\\1&0\end{bmatrix}$ then the matrix AB is equal to

$\begin{bmatrix}0&1\\-1&0\end{bmatrix}$

The correct answer is Option (3) → $\begin{bmatrix}0&1\\-1&0\end{bmatrix}$

$A=\begin{pmatrix}1&0\\0&-1\end{pmatrix},\quad B=\begin{pmatrix}0&1\\1&0\end{pmatrix}$

$AB=\begin{pmatrix} 1\cdot0+0\cdot1 & 1\cdot1+0\cdot0\\ 0\cdot0+(-1)\cdot1 & 0\cdot1+(-1)\cdot0 \end{pmatrix}$

$AB=\begin{pmatrix}0&1\\-1&0\end{pmatrix}$

The matrix $AB$ is $\begin{pmatrix}0&1\\-1&0\end{pmatrix}$.