Derivative f:GLn(R)→GLn(R):A↦A−1

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manpreet Tuteehub forum best answer Best Answer 3 years ago

Given a continuous f:GLn(R)GLn(R):AA1f:GLn(R)→GLn(R):A↦A−1, I want to show that for gGLn(R)g∈GLn(R) the derivative Df(g)Df(g) equals

Hg1Hg1H↦−g−1Hg−1

for HMat(n,R)H∈Mat(n,R).

 

I tried proving

limXA||f(X)
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