Let $A$ be a $2 × 2$ matrix with complex entries which is non-zero and non-diagonal. Pick out the cases when $A$ is diagonalizable.
- (a) $A^2 = I$.
- (b) $A^2 = 0$.
- (c) All eigenvalues of $A$ are equal to $2$.
(a) is true since eigen values are distinct. But what about (b) and (c)?