If A and B are 4 X 4 matrices detA 1 detB 3 then Solution

If A and B are 4 X 4 matrices, det(A) = - 1, det(B) = 3, then

Solution

Given that

1 ) det ( A ) = -1 , det ( B ) = 3

det ( AB ) = det ( A ) det ( B )

= -1 x 3

= -3

Therefore,

det ( AB ) = -3

2 ) det ( -2A ) = (-2)⁴ det ( A ) [ 4 = order of matrix ]

= 16 x -1

= -16

3 ) det ( A^T ) = det ( A )

= -1

4 ) det ( B^-1 ) = 1 / det ( B )

= 1 / 3

5 ) det ( B² ) =( det B )²

   = ( 3 ) ²

   = 9