# Thread: Proof of (A^-1)^-1 = A

1. ## Proof of (A^-1)^-1 = A

I am studying for my exam on tuesday and my professor in class on friday told us to make sure how to prove this:

$(A^{-1})^{-1} = A$

Can i get some help proving this in the easiest way possible

2. Originally Posted by mybrohshi5
I am studying for my exam on tuesday and my professor in class on friday told us to make sure how to prove this:

$(A^{-1})^{-1} = A$

Can i get some help proving this in the easiest way possible

As by definition $X^{-1}$ is the inverse of $X$ , we get that $\left(A^{-1}\right)^{-1}$ is the
inverse of $A^{-1}$ . But we know that $AA^{-1}=A^{-1}A=I$ , and now use uniqueness of inverses...