Commuting Matrices

Two matrices and which satisfy

(1)

under matrix multiplication are said to be commuting.

In general, matrix multiplication is not commutative. Furthermore, in general there is no matrix inverse even when . Finally, can be zero even without or . And when , we may still have , a simple example of which is provided by

			(2)
			(3)

for which

(4)

but

(5)

(Taussky 1957).