Chapter 6 - Summary, Review, and Test - Review Exercises - Page 657: 37

No

We are given the matrices: $A=\begin{bmatrix}2&7\\1&4\end{bmatrix}$ $B=\begin{bmatrix}4&-7\\-1&3\end{bmatrix}$ Compute $AB$: $AB=\begin{bmatrix}2&7\\1&4\end{bmatrix}\begin{bmatrix}4&-7\\-1&3\end{bmatrix}$ $=\begin{bmatrix}8-7&-14+21\\4-4&-7+12\end{bmatrix}$ $=\begin{bmatrix}1&7\\0&5\end{bmatrix}$ Because $AB\not=I_2$, $B$ is not the inverse of $A$.