Question

Which statement describes the general relationship between \[AB\] and \[BA\]?

Options

• If \[AB\] exists, then \[BA\] must be the zero matrix.

• \[AB\] and \[BA\] are always both defined and equal.

• \[AB \neq BA\] in general, and sometimes one product may not even be defined.

• \[AB = BA\] always.

Answer 1

In general, \[AB \neq BA\], so matrix multiplication is not commutative. Also, the size condition for \[AB\] can hold while the condition for \[BA\] does not hold.