Explain why the operations on congruence classes p,[a]+[b]=[a+b] and [a][b]=[a b], are well defi

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Step 1: Understand the definition of congruence classes modulo u005C( p u005C).u000Au002D Two integers u005C( a u005C) a

Explain why the operations on congruence classes $\bmod p,[a]+[b]=[a+b]$ and $[a][b]=[a b]$, are well defined. That is, why does the result not depend on the particular choice of $a$ and $b$ from the congruence class?