##### 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 \(B=0\text{.}\)