In each case either prove the assertion or give an example showing that it is false. (a)

Question:

In each case either prove the assertion or give an example showing that it is false.
(a) If A and B are both invertible, then A + B is invertible.
(b) If A4 = 3I, then A is invertible.
(c) If AB = B for some B ≠ 0, then A is invertible.
(d) If A2 is invertible, then A is invertible.