Question

For \[\mathbf{A}=\begin{bmatrix}2&3\\1&2\end{bmatrix}\] and \[\mathbf{B}=\begin{bmatrix}2&-3\\-1&2\end{bmatrix}\], what is \[\mathbf{A}\mathbf{B}\]?

Options

• \[\begin{bmatrix}0&1\\1&0\end{bmatrix}\]

• \[\begin{bmatrix}4&-6\\2&-3\end{bmatrix}\]

• \[\begin{bmatrix}1&0\\0&-1\end{bmatrix}\]

• \[\begin{bmatrix}1&0\\0&1\end{bmatrix}\]

Answer 1

Multiplication gives entries \(4-3\), \(-6+6\), \(2-2\), and \(-3+4\). Thus \(\mathbf{A}\mathbf{B}=\begin{bmatrix}1&0\\0&1\end{bmatrix}=I\).