If A and B are 4x4 matrices, det(A) = -4, det(B) = 3, then (f) det(A(B^T)^-1) = ???,

Expert Answers
mvcdc eNotes educator| Certified Educator

First, note that solving for determinants is distributive:

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


`det(A(B^T)``^-1) = det(A) det((B^T)^-1)` 

` `

Then, note the following:

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

ii. The determinant of the transpose of a matrix is just the determinant of the original matrix.


`det((B^T)^-1) = 1/det(B^T) = 1/det(B) = 1/3` 

Therefore, the answer you are looking for is:

`det(A(B^T)^-1) = -4 * (1/3) = -4/3.`


pramodpandey | Student

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