Proof: The identity matrix is invertible and the inverse of the identity is the identity How can i show that: $II^{-1} = I = I^{-1}I$ (the identity matrix is invertible) for all cases. And then proof that: $I^{-1} = I$ (The inverse of the identity is the identity). I don't know how start both proof, any suggestion?
Suppose $A$ is the inverse of the identity matrix. Then $AI =IA =  I$. But $AI = IA = A$ as well so $A=I$.
AS INVESE OF ANY MATRIX IS GIVEN BY A FORMULA; A-1=[1/|A|]X[ADJ OF A]
BUT HERE WE PROOF BY GENERAL METHOD.
                                      LET  K IS INVERSE OF IDENTITY MATRIX I THEN 
                         WE KHOW THAT AS, KI=IK=I
                                     ALSO,KI=IK=K
                                       SO,I=K  OR  [I=I-1]

SO INVERSE OF IDENTITY MATRIX IS IDENTITY MATRIX.

                                ** THANKS**