Let A and B be n-square matrices. Answer true or false:
(a) If A^2 = 0, then A = 0.
(b) If A^2 = 0 and λ is an eigenvalue of A, then λ = 0.
(c) If A^2 = 0, then the rank of A is at most 2.
(d) If A^2 = A, then A = 0 or I.
(e) If A*A = 0, then A = 0.
(f) If AB = 0, then A = 0 or B = 0.
(g) If |AB| = 0, then |A| = 0 or |B| = 0.
(h) AB = BA.
(i) |AB| = |BA|, where A is m × n and B is n × m.
(j) |A + B| = |A| + |B|.
(k) (A + I)^2 = A^2 + 2A + I.
(l) |kA| = k|A| for any scalar k.