Question

A is a 3x3 matrix with det(A) = 4. Find det(adj(A)).

Answer 1

The value of det(adj(A)) is 16.

Explanation:

It is given that A is a 3x3 matrix with det(A) = 4.

We need to find the value of det(adj(A)).

We have a formula

`det(adj(A))=(det(A))^(n-1)`

where, n is order of the square matrix.

Substitute det(A) = 4 and n=3 in the above formula.

`det(adj(A))=(4)^(3-1)`

`det(adj(A))=(4)^(2)`

`det(adj(A))=16`

Therefore, the value of det(adj(A)) is 16.