Inverse and Determinant of a Matrix Practice Test

Two transforms are $A=\begin{bmatrix}1&2\3&4\end{bmatrix}$ and $B=\begin{bmatrix}2&4\1&2\end{bmatrix}$. Since invertible means $\det\neq0$, which of these matrices is invertible?

A coordinate change uses $A=\begin{bmatrix}0&2\-1&3\end{bmatrix}$. Using $A^{-1}=\frac1{ad-bc}\begin{bmatrix}d&-b\-c&a\end{bmatrix}$, calculate the inverse of $A$, if possible.​