Exercise 4.3.10

Answers

If $M$ is nilpotent, we say $M^{k} = O$ for some positive integer $k$ . So we have

0 = \det (O) = \det (M^{k}) = {(\det (M))}^{k} .

This means that $\det (M)$ must be zero.

jephianlin

2011-06-27 00:00