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I would like to get some help with finding the derivative of the next function:
$F: GL(n,\mathbb{R}) \mapsto GL(n,R) $ , defined by $F(A)=A^{-1} $.
One can try find the derivative of the known formula for finding inverse of a metrix by
$A^{-1}=\frac{1}{det(A)} adj(A) $
I tried to be sophisticated , using the inverse function formula, but the inverse of the given function, as I see it, is just the same function. Is that right?

Ron Abramovich
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    I'm not sure why this question has been associated with that one, they're not asking the same thing. Voting to reopen. – Ninad Munshi Oct 08 '20 at 12:13
  • The derivative will be some rank $4$ tensor that will resemble something like $-A^{-2}$ but with many more components. But in index notation this is not difficult to convey. – Ninad Munshi Oct 08 '20 at 12:32
  • @NinadMunshi The derivative is given there by the multipication derevative formula. You guys are right about the tensor dimension of the derivative, which nowadays i'm not realy know how to cope with. – Ron Abramovich Oct 08 '20 at 12:36

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