If A is 4x4 matrix and  det(A) = -4. Then  det(8A^-1) = ???,

Expert Answers
mvcdc eNotes educator| Certified Educator

We are given the following:

det(A) = -4

det(B) = 3

To solve for det(8A^-1), we first note the following:

i. The determinant of an inverse of a matrix, is just the reciprocal of the determinant of the original matrix.

ii. Scalar multiplication of a row by a constant c, also multiplies the determinant by c.

Hence, det(8A^-1) can be calculated as follows:

`det(8A^-1) = 8^4 det(A^-1) = 8^4 (1/det(A)) = 4096/-4 = -1024`


Note that we multiplied by 8^4 since A is a 4 x 4 matrix (i.e. there are 4 rows, each of which is multiplied by the scalar 8, thus, the determinant of A^-1 is multiplied to 8 for times or 8^4).

pramodpandey | Student

We know


`det(xP)=x^ndet(P)`    , x is scalar and  n is order of P.