Linear Algebra How to find a matrix with the property A3A an

Linear Algebra: How to find a matrix with the property A³=A and how to find a matrix with the property A³=-A.

I can not use a 0 matrix or a diagonal matrix. I was given the hint to use diagonlization but I am not sure how to go about doing this. Any help?

Solution

we can find out it with inversion of the matrix.