Find all $2 \times 2$ matrices $\bold{A}$ that have the property that for any $2 \times 2$ matrix $\bold{B}$,

Question

\[\bold{A} \bold{B} = \bold{B} \bold{A}.\]

Answer 1

Recall that Matrix multiplication is always commutative if ...

... one matrix is the Identity matrix.
... one matrix is the Zero matrix.
... both matrices are 2×2 rotation matrices. (basically case #2)
... both matrices are Diagonal matrices.