##### 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