If A and B are 3 times 3 matrices with detA 5 and detB 7 f

If A and B are 3 times 3 matrices with det(A) = 5 and det(B) = 7, find the determinants of the matrices AB and -2A. det(AB) = det(-2A)

Solution

det(AB) = det(A) det(B) , this is property of determinants only when A and B are of the same order.

So, det(AB) = det(A) . det(B) = 5 X 7 = 35

And

the property used here is det(kA) = kⁿ det(A), where is k is some constant and n is the order of the determinant.

det(-2A) = -det(2A) = -(2)³ det(A) = -8 X 7 = -56