The multiplicative inverse of a number 'A' (modulo M) is another number 'x' such that when you multiply them together, the remainder is 1 when divided by M.

The relationship is written as: A ⋅ x ≡ 1 (mod M)

Condition for Existence: A multiplicative inverse for A (mod M) exists only if A and M are coprime. This means their greatest common divisor (GCD) is 1.

For example, the inverse of 3 (mod 11) is 4 because (3 * 4) = 12, and 12 mod 11 = 1.

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