• Sep 24th 2009, 10:40 AM
forensic91
Hello, I had 3 homework problems that I am having trouble with. I really have problems when it comes to proving things. Here goes

Assume A is an n x n invertible matrix. Prove the following identities:

c) adj(k*A) = k^(n-1) * adj(A), k E Real Number.

So I've tried a bit, starting out with

A^-1 = 1/det(a) * adj(a) then
A^(-1) * det(a) = adj(a) then I do the trace of both sides and don't really know where to go from there...

CAn anyone help me out?
• Sep 24th 2009, 10:55 PM
NonCommAlg
Quote:

Originally Posted by forensic91
Hello, I had 3 homework problems that I am having trouble with. I really have problems when it comes to proving things. Here goes

Assume A is an n x n invertible matrix. Prove the following identities:

c) adj(k*A) = k^(n-1) * adj(A), k E Real Number.

So I've tried a bit, starting out with

A^-1 = 1/det(a) * adj(a) then
A^(-1) * det(a) = adj(a) then I do the trace of both sides and don't really know where to go from there...

for a) and c) use the definition of adjoint matrix (cofactors!). part b) is trivial because: $I=\text{adj}(AA^{-1})=\text{adj}(A^{-1}) \text{adj}(A).$