If A and B are 2 times 2 matrices det A 2 det B 5 then det

If A and B are 2 times 2 matrices, det (A) = -2, det (B) = -5, then det (AB) =, det (3A) =, det (A^T) =, det (B^-1) =, det (B^4) = .

Solution

det (AB) = det(A)*Det(B) = -2*-5 = 10. When A is a nxn matrix, then det(cA) = cn det(A). Here, det(3A) = 32*-2 = -18. det(AT) = det(A) = -2. we know that 1 = det(I) = det( BB-1) = det(B)det(B-1) so that det(B-1) = 1/det(B) . Here, det(B-1)= -1/5. det(B4) = det(B.B.B.B) = det(B).det(B).det(B).det(B) = [det(B)]4. Here, det(B4) = (-5)4 625.