How do I prove or show this? Not sure how to go about it.

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- Apr 2nd 2009, 03:39 PMCrakaIf matrix A is invertible then so it it transpose A^t
How do I prove or show this? Not sure how to go about it.

- Apr 2nd 2009, 04:13 PMo_O
If you can prove that both: $\displaystyle A^T \left(A^{-1}\right)^T = \left(A^{-1}\right)^T A^T = I$

then by definition, we've shown that $\displaystyle A^T$ is invertible.

So for: $\displaystyle A^T \left(A^{-1}\right)^T = I$

Use the fact that: $\displaystyle X^TY^T = (YX)^T$

So we see that: $\displaystyle A^T\left(A^{-1}\right)^T = \left(A^{-1}A\right)^T = I^T = I$

Now finish off by proving the other.