For two nonsingular matrices A and B, check numerically the identity: det(A · B) = det(A) det(B). For this purpose, (a) generate two random 2D matrices A and B of order n = 100; (b) use routine Gauss...

For two nonsingular matrices A and B, check numerically the identity:

det(A · B) = det(A) det(B).

For this purpose, (a) generate two random 2D matrices A and B of order n = 100; (b) use routine Gauss to calculate det(A · B) and det(A) det(B); and (c) check the vanishing of the relative difference between the two expressions.