Thread: Adjoints and Determinants Help

Adjoints and Determinants Question?

1) Let A be a 3x3 matrix with determinant -12.

a) What is det(adj(A^T))?
b) What is det(adj(A^-1))?
c) What is det(adj(3A))?

2) Let A be a 2x2 matrix such that adj(A) =

[8, -1]
[-5, -4]

What is det(A)?

It can be shown that:

So for #1, just use this directly and simplify using your properties of determinants:
(a):

(b):

(c):

For #2, modifying the property I gave you earlier, we get:

So find the determinant of your adjoint matrix and then take its (n-1)-th root.