What would you like to understand?

18 is its own inverse modulo 19 because 18 is congruent to -1 modulo 19, and -1 is always its own multiplicative inverse since $(-1)(-1)=1$. Therefore, $18 \cdot 18 \equiv (-1)(-1) \equiv 1 \pmod{19}$.

Conditions: Working modulo 19.; Using the fact that 18 ≡ -1 (mod 19).

18 is its own inverse modulo 19 because 18 is congruent to -1 modulo 19, and -1 is always its own multiplicative inverse since $(-1)(-1)=1$. Therefore, $18 \cdot 18 \equiv (-1)(-1) \equiv 1 \pmod{19}$.

Conditions: Working modulo 19.; Using the fact that 18 ≡ -1 (mod 19).