Thread: finding determinant of inverse

Let A = (aij)n x n and the determinant of A does not equal zero. Find det(A^-1) in terms of det A.

Honestly, I have no idea where to start. If someone could get me going in the right direction with a suggested course of action, I think it would be enough. Thank you!

See here.

Originally Posted by dan213

Let A = (aij)n x n and the determinant of A does not equal zero. Find det(A^-1) in terms of det A.

Honestly, I have no idea where to start. If someone could get me going in the right direction with a suggested course of action, I think it would be enough. Thank you!

It is `well known' that det(AB)=det(A)det(B) for A, B square matrices. If you do not have this result in your notes it would be a good exercise for you to prove it.

Can you think how this result might apply to your problem?