In each case either show the statement is true, or give an example showing that it is

Question:

In each case either show the statement is true, or give an example showing that it is false.
(a) If AJ = A, then J = I.
(b) I is symmetric, then I + A is symmetric.
(c) If A ≠ 0, then A2 ≠ 0.
(d) If A commutes with A + B, then A commutes with B.
(e) If AB has a column of zeros, so also does B.
(f) If AB has a row of zeros, so also does A.