Question

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

Answer 1

Answer:

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

Step-by-step 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.