- #1
pyroknife
- 613
- 3
Show that if A is invertible, then At is invertible
and (At )-1
= (A-1)t .
If A is invertible, then det(A)≠0
det(A)=det(A^t)
thus det(A^t)≠0
I'm not really sure how to prove the second part. It's an identity that I remembered, but don't know how to prove.
I'll take a crack at it though:
Multiply A^t to both sides
gives I=A^t (A^-1)^t
For the RHS, can i multiply A^t to A^-1 or does the ^t prevent me from doing that?
and (At )-1
= (A-1)t .
If A is invertible, then det(A)≠0
det(A)=det(A^t)
thus det(A^t)≠0
I'm not really sure how to prove the second part. It's an identity that I remembered, but don't know how to prove.
I'll take a crack at it though:
Multiply A^t to both sides
gives I=A^t (A^-1)^t
For the RHS, can i multiply A^t to A^-1 or does the ^t prevent me from doing that?