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)?
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.