Exercise 33.
We define the trace of a \(2 \times 2\) matrix to be the sum of its diagonal entries. That is, the trace of
\begin{equation*}
A
=\begin{pmatrix}
a & b \\
c & d
\end{pmatrix}
\end{equation*}
is \(\trace(A) = a + d\text{.}\) Show that \(\trace(AB) = \trace(BA)\) for any \(2 \times 2\) matrices \(A\) and \(B\text{.}\)