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

Question:

In each case either prove the statement or give an example showing that it is false:
(a) If A is invertible and adj A = A-1, then det A = 1.
(b) If det A ≠ 0 and AB = AC, then B = C.
(c) If adj A = 0, then A = 0.
(d) If A has a row of zeros, so also does adj A.
(e) det(I + A) = 1 + det A.
(f) If det A = 1, then adj A = A.