Question

If A = N x N and * be any binary operation on A defined by

(a, b) * (c, d) = (a + c, b + d), then the binary operation is

• A. Associative
• B. Commutative
• C. Commutative and associative
• D. Commutative but not associative

Answer 1

The correct option is C

Commutative and associative

(a, b) * (c, d) = (a + c, b + d) and

(c, d) * (a, b) = (c + a, d + b) = (a + c, b + d) = (a, b) * (c, d)

So, * is commutative.

(a, b) * [(c, d) * (e, f)] = (a, b) * (c + e, d + f) = (a + c + e, b + d + f) and

[(a, b) * (c, d)] * (e, f) = (a + c, b + d) * (e, f) = (a + c + e, b + d + f).

So, * is associative also.