Construct a random 4 ( 4 matrix A with integer entries between - 9 and 9, and

Question:

Construct a random 4 ( 4 matrix A with integer entries between - 9 and 9, and compare det A with det AT, det (-A), det(2A), and det(10 A). Repeat with two other random 4 ( 4 integer matrices, and make conjectures about how these determinants are related. (Refer to Exercise 36 in Section 2.1) Then check your conjectures with several random 5 ( 5 and 6 ( 6 integer matrices. Modify your conjectures, if necessary, and report your results?