If n is an integer that is NOT a multiple of 3, then n^2 = 1 mod 3

I did ...

to the contrary, if n is a multiple of 3 then n = 0 mod 3

then n^2 is also a multiple of 3 -> n^2 = 0 mod3 reaching a contradition

---> <---- therefore n^2 = 1mod 3 when n is not a multiple of 3. QED.

Is this correct?