True: $a^2=b^2\!\!\!\pmod n \Longleftrightarrow (a-b)(a+b)=0\!\!\!\pmod n$ $\Longleftrightarrow a-b=0\!\!\!\pmod n\,\,\,or\,\,\,a+b=0\!\!\!\pmod n$ , since n is prime.