Let A be Q/{1}. Define * on A by x * y=x+y-xy. Is * binary on A? If so, examine the existence of identity & inverse properties for the operation * on A.

Let A be Q/{1}. Define * on A by x * y=x+y-xy. Is * binary on A? If so, examine the commutative and association properties satisfied by * on A.

(i) Let M={({:(x,x),(x,x):}):x in R -{0}} and let ** be the matrix multiplication. Determine whether M is closed under ** . If so, examinie the existence of identity, existence of inverse properties for the operation ** on M.

Let M={[{:(,x,x),(,x,x):}}: x in R-{0}} and let * be the matrix multiplication. Determine whether M is closed under *. If so, examine the existence of identify, existence of inverse properties for the operation * on M.

Define an operation * on Q as follows: a * b =((a+b)/(2)), a, b in Q . Examine the existence of identify and existence of inverse for the operation * on Q.

Let S=Q-(1) and is defined in S as a ** b =a+b-ab for all a,b, in G . Verify existence of identity .

Verify (i) closure property (ii) commutative property (iii) associative property (iv) existence of identity and (v) existence of inverse for the operation xx_(11) on a subset A = {1,3,4,5,9} of the set of remainders {0,1,2,3,4,5,6,7,8,9,10}.