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 det A = 0, then A has two equal rows.
(b) If R is the reduced row-echelon form of A, then det A = det R.
(c) det(AT) = -det A.
(d) If det(A) = det(B) where A and B are the same size, then A = B.