If $A = \begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}$, $B = \begin{bmatrix}x & 2 \\ 3 & 7\end{bmatrix}$ and $AB = BA$, what is $x$?

Explanation

1. 01

   Row 1, column 2 of $AB$ is $1(2) + 2(7) = 16$; of $BA$, $x(2) + 2(4) = 2x + 8$.

2. 02

   $2x + 8 = 16$ gives $x = 4$, and row 2, column 1 agrees: $3x + 12 = 24$.