Question

Give an example of two 2×2 matrices A and B, neither of which is the zero matrix or the identity matrix, such that AB=BA.

Answer 1

Let

$A=B=\begin{bmatrix}0&1\\1&0\end{bmatrix}$

Then

$AB=BA=\begin{bmatrix}0&1\\1&0\end{bmatrix}^2=\begin{bmatrix}1&0\\0&1\end{bmatrix}$