Find the value of $k$ if $AB=BA$

Question

$A=\begin{bmatrix} 2 & 6\\ 3 & 5 \end{bmatrix}$

$b=\begin{bmatrix} 1 & 0\\ 0 & k \end{bmatrix}$

Both are $2×2$ matrices. I have multiplied it but that's where I get stuck.

Answer 1

Notice that when $k=1$, $B$ is the identity matrix which satisfies $AB=BA$, and is the only $k$ value that satisfies $AB=BA$.