Matrices & Systems · Medium problem

Two sequential operations are applied to a $2$-dimensional resource vector: operation $A = \begin{pmatrix}2&1\\0&3\end{pmatrix}$ and operation $B = \begin{pmatrix}1&k\\4&5\end{pmatrix}$, where $k$ is one entry of $B$ that hasn't been measured yet. For most values of $k$, applying $A$ then $B$ gives a different row $1$, column $2$ result than applying $B$ then $A$. Find the value of $k$ at which the two orders happen to agree in that entry.