If you fill in n=1, you'll get .
That does not look like the identity matrix.
So no, it is not n=1.
If you're using matlab you might simply iterate over n, calculate A^n and see if it matches the identity matrix.
Using a little math would be to calculate the eigenvalues.
If any of them has an absolute value that deviates from 1, it is not possible.
Then you need to find the lowest integer power that will turn all eigenvalues into 1.
If there is one, that is your prime candidate.
You will still have to verify if it fits.