(adsbygoogle = window.adsbygoogle || []).push({}); Given that [itex]A^2[/itex] is invertible, does it neccesarily mean that

[tex]\left(A^2\right)^{-1}\,=\,\left(A^{-1}\right)^2[/tex]?

I know that this is true, but I have no idea on where to even start a proof of this!

Maybe:

[tex]\left(A^2\right)^{-1}\,=\,\left(A\,A\right)^{-1}[/tex]

But how would I operate on infinite matrices (i.e. - [itex]a_{i\,j}[/itex])?

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# Homework Help: LINEAR ALG.: A^2 is invertible, is the inverse of a^2 equal to the square of inv(A)?

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