Things to be careful of

The following properties hold for real numbers but not for matrices.

Commutativity:

It is not generally true that \(AB = BA\text{.}\)

Cancellation:

It is not generally true that \(AB = AC\) implies that \(B = C\text{.}\)

Zero divisors:

It is not generally true that \(AB = 0\) implies that either \(A=0\) or \(B=0\text{.}\)

in-context