Related InterviewSolutions

• Let * be a binary operation on set `Q-[1]`defined by `a*b=a+b-a b`for all`a , b in Q-[1]dot`Find the identity element with respect to `*onQdot`Also, prove that every element of `Q-[1]`is invertible.
• Let `A=Q x Q`and let * be a binary operation on A defined by`(a , b)*(c , d)=(a c , b+a d)`for `(a , b),(c , d) in Adot`Then, with respect to * on AFind the identity element in AFind the invertible elements of A.
• On Q, the set of all rational numbers, a binary operation * is definedby `a*b=(a b)/5`for all `a , b in Qdot`Find the identity element for * in Q. Also, prove that every non-zeroelement of Q is invertible.
• Define a binary operation * on the set `A={1,2,3,4}`as `a*b=a b`(mod 5). Show that 1 is the identity for * andall elements of the set A are invertible with`2^(-1)=3`and `4^(-1)=4`
• If * is defined on the set R of all real numbers by `a*b=sqrt(a^2+b^2)`, find the identity element in R with respect to *.
• Let S be the set of all rational numbers except 1 and * be defined on Sby `a*b=a+b-a b ,`for all`a , b in Sdot` Find its identity element