Verify that det AB = (det A)(det B), where the matrices A and B are given below. 30 20 A = B = 61 5 4 Calculate det A and det B. det A 3, det B=8 (Simplify your answers.) Now calculate the product (det A)(det B). (det A)(det B) 24 (Simplify your answer.) Calculate the product of matrices AB. AB = 60 17 4 (Type an integer or decimal for each matrix element.) Now calculate the determinant of the product of matrices A and B. det (AB) (Simplify your answer.)

Use elementary matrices to find the inverse of A=100010abc, c0.

Show that A and B are inverse matrices if A = - 1 -2 2 0 1 -5 0 0 and B = 2-1 52 5 -2 -1 -2 6 2 2 5 Select the correct choice below and fill in any answer boxes to complete your choice. (Simplify your answers. Type an integer or simplified fraction for each matrix element.) OA. The matrices A and B are inverses because A - B = OB. The matrices A and B are inverses because A + B = Oc. The matrices A and B are inverses because AB = and B-A= and B+A= and BA = K S

Please answer both. Thank you.