First, you have calculated the derivative incorrectly- you forgot the main diagonal.
That will be 0 if and only if (p-1)[a (mod p)]= 1.
Any help with the following problem is greatly appreciated:
For the part (a) of this problem, I must show that belongs to the general linear group of 2x2 matrices over p (a prime) iff .
I know from a definition that .
So here we must have
I'm kind of stuck here, what can I do next?
Thanks, that was a typo. So, we must have that . So I guess must be equal to in . Therefore .
But how do I prove that (p-1)=-1?
And for part (b) I think they are asking for the inverse of
Then the inverse would be of the form:
But what values do I use for and 10 mod p?