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)?

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- Nov 16th 2008, 09:51 PMMy Little PonyAdjoints 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)? - Nov 16th 2008, 10:06 PMo_O
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.