Q 1: Let A = N x N and let * be a binary operation on A defined by (a,b)*(c,d) = (ac, bd). Show that (A,*) is associative. Answer:

Q 2: Let a * b be a binary operation on N given by a * b = l.c.m (a,b), a, b, € N, find 2*4 2 8 4

Q 3: For I = (2,1,0,1,2) and the binary operation of addition defined on I, ehat is the inverse of 2. 0 2 1

Q 4: Let a*b = l.c.m of (a,b), a, b € N, find 3*5 12 8 15

Q 5: Find the identity element on a*b = a+ab, a, b € 1 Answer:

Q 6: Let * be a binary operation defined on Q. Check if a*b = ab, for a,b € Q is commutative. Yes No

Q 7: Let * be a binary operation defined on Q. Check if a*b = a^{2}+b^{2}, for a,b € Q is commutative. Yes No

Q 8: Find the identity element if a*b = a+b+ab , a, b € 1 Answer:

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