Inverse of any identity matrix

Question

Is it true that the inverse of any identity matrix is itself? From my working, It appeared true for 1x1's to 3x3's. If it is true, Why is this the case?

Thanks

EDIT: Thanks for the answers. I understand it now

Answer 1

What matrix do you need to multiply an identity matrix with to get an identity matrix?:) I think it’s obvious from here

Answer 2

For any matrix $A$, the matrix $B$ is the inverse of $A$ if $A\cdot B = B\cdot A = I$, where $I$ is the identity matrix. Since $I\cdot I = I$ by definition, then the matrix $I$ is the inverse of the matrix $I$.