Another Linear Algebra Question

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SUMMARY

The discussion focuses on proving that if matrix A is nonsingular, then its transpose A^T is also nonsingular, and that the inverse of the transpose (A^T)^-1 equals the transpose of the inverse (A^-1)^T. The hint provided, (AB)^T = B^T*A^T, is crucial for understanding the proof. The user seeks assistance in visualizing the problem and starting from the equation (A^{-1}A)^T=I.

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I am having to do a proof on a problem and am not really seeing it for some reason. Maybe it's because I have been doing the homework for so long.

Prove that if A is nonsingular then A^T is nonsingular and

(A^T)^-1 = (A^-1)^T

Hint: (AB)^T = B^T*A^T

I understand the hint, but I can't seem to get an image of the actual problem.

Can anyone help me?
 
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Start from [itex](A^{-1}A)^T=I[/itex].
 

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