On my exam today there's this question:
A is a real n by n matrix and it is its own inverse. Prove that A is diagonalizable.
It seems very few students solved it if any.
All I know is that it's eigenvalue has to be 1 or -1. But how do I know the dimension of the eigenspace is enough? I've searched through internet and the solutions I found is all about minimal polynomial which I haven't learnt. Is there any method using only properties of eigenvectors?