38 views

Answer whether the following statements are True or False.

For a nilpotent matrix $A \in \mathrm{M}_{n}(\mathbb{R})$, let
$\exp (A):=\sum_{n=0}^{\infty} \frac{A^{n}}{n !}=\mathrm{Id}+\frac{A}{1 !}+\frac{A^{2}}{2 !}+\cdots \in \mathrm{M}_{n}(\mathbb{R})$
If $A$ is a nilpotent matrix such that $\exp (A)=\mathrm{Id}$, then $A$ is the zero matrix.

1
117 views