(A) Prove or Disprove: If a ≡ B (Mod 5) $a ^ { 2 } \equiv b ^ { 2 } ( \bmod 5 )$

Essay

(a) Prove or disprove: If a ≡ b (mod 5), where a and b are integers, then $a ^ { 2 } \equiv b ^ { 2 } ( \bmod 5 )$ (b) Prove or disprove: If $a ^ { 2 } \equiv b ^ { 2 } ( \bmod 5 )$ where a and b are integers, then a ≡ b (mod 5).