I am studying for my exam on tuesday and my professor in class on friday told us to make sure how to prove this:
$\displaystyle (A^{-1})^{-1} = A $
Can i get some help proving this in the easiest way possible
Thanks in advanced!
As by definition $\displaystyle X^{-1}$ is the inverse of $\displaystyle X$ , we get that $\displaystyle \left(A^{-1}\right)^{-1}$ is the
inverse of $\displaystyle A^{-1}$ . But we know that $\displaystyle AA^{-1}=A^{-1}A=I$ , and now use uniqueness of inverses...
Tonio