Please determine if the following statements are true or false, and explain why.

PYObLEVl/L 1: Decide whether the following statements are true of false. If a statement is true, explain why it is true. If a statement is false, give an example to show that it is false. All matrices below are square matrices. 1. 'x'lChCrb-OJ If A and B are n X 71 square matrices and det(B) = 3" det(A), then B = 3A. . A is a 4 x 4 matrix with det(A) = 0, then A must have a column of zeros, or a row of zeros, or two identical rows, or two identical columns. . If B is the row reduced echelon form of A, then det(A) = det(B). . det(A) = det(B) 4:) A = B. . det(A i B) = det(A) i det(B). . If det(AB) = 1, then AB = I and so A = Bl. . If A % O, B % O and C g O with AB = A0, then det(A) 7 0