Let A be an $n\times n$ matrix with complex entries which is not a diagonal matrix. Pick out the cases when A is diagonalizable. (a) A is idempotent. (b) A is nilpotent. (c) A is unitary.
I think (c) is true. and (b) is false .not sure about (a), though order $2$ idempotent matrices are diagonalizable since it has two distinct eigenvalues $0,1$.but what is the general case .