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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We know is invertible, and so Taking the transpose of both sides gives What can you then conclude about the invertibility of
So then can I just say, since these two are equal A transpose is invertible. Then it's inverse is A inverse times A.
Originally Posted by widenerl194 So then can I just say, since these two are equal A transpose is invertible. Then it's inverse is A inverse times A. No, , not . What you can say is that the inverse of A transpose is the transpose of A inverse.
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