I have this problem:
$A$ is an $n \times n$-matrix, its characteristic polynomial is $P(X)=(X-1)^n$. Prove that $A$ is similar to its inverse.
How do you solve it? I really don't know.
inverselinear algebramatrices
I have this problem:
$A$ is an $n \times n$-matrix, its characteristic polynomial is $P(X)=(X-1)^n$. Prove that $A$ is similar to its inverse.
How do you solve it? I really don't know.
Best Answer
Hints. Call the underlying field $\mathbb{F}$. We will use the following fact: