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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- Mar 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! - Mar 13th 2013, 08:16 PMGusbobRe: Linear Algebra Proof with invertible matrices
We know $\displaystyle A$ is invertible, and so $\displaystyle A^{-1}A=I$

Taking the transpose of both sides gives $\displaystyle A^T(A^{-1})^T=I$

What can you then conclude about the invertibility of $\displaystyle A^T?$ - Mar 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.

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