1. Two results that apply to scalars that students are tempted to apply to matrices are

the following.

• If ab = ac and a 0, then b = c(cancellation law).

• ab = 0 if and only if a = 0 or b=0.

These results do not extend to matrix arithmetic, in general.

(a) Find matrices A, B and C such that AB = AC and A ‡ 02×2 but B‡ C. Justify

your choices.

(b) Find matrices A and B such that A ‡ 02x2 and B # 02x2 but AB = 02x2. Justify

your choices.

Recall that 02x2 represents 2 x 2 zero matrix.