I don't even know where to start with this:

Let A be an n x n invertible matrix. Prove that A^{T}is invertible and determine its inverse in terms of A^{-1.}

Any hints or suggestions would be appreciated!

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- March 13th 2013, 07:38 PMwidenerl194Linear Algebra Proof with invertible matrices
I don't even know where to start with this:

Let A be an n x n invertible matrix. Prove that A^{T}is invertible and determine its inverse in terms of A^{-1.}

Any hints or suggestions would be appreciated! - March 13th 2013, 08:16 PMGusbobRe: Linear Algebra Proof with invertible matrices
We know is invertible, and so

Taking the transpose of both sides gives

What can you then conclude about the invertibility of - March 14th 2013, 12:49 PMwidenerl194Re: Linear Algebra Proof with invertible matrices
So then can I just say, since these two are equal A transpose is invertible. Then it's inverse is A inverse times A.

- March 14th 2013, 02:24 PMHallsofIvyRe: Linear Algebra Proof with invertible matrices