Define a binary operation * on the set `A={0,1,2,3,4,5}` given by `a\**b=a b (mod 6) `. Show that 1 is the identity for *. 1 and 5 are the only invertible elements with `1^(-1)=1` and `5^(-1)=5`

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 ** and all elements of the set A are invertible with 2^(-1)=3 and 4^(-1)=4.

Define a binary operation * on the set A={0,\ 1,\ 2,\ 3,\ 4,\ 5} as a * b=a+b(mod 6) Show that zero is the identity for this operation and each element a of the set is invertible with 6-a being the inverse of adot

Define a binary operation * on the set A={0,1,2,3,4,5} as a*b=a+b (mod 6). Show that zero is the identity for this operation and each element a of the set is invertible with 6-a being the inverse of adot OR A binary operation * on the set {0,1,2,3,4,5} is defined as a*b={a+b ,ifa+b<6a+b-6,ifa+bgeq6 Show that zero is the identity for this operation and each element a of set is invertible with 6-a , being the inverse of a.

Define a binary operation * on the set A={0,1,2,3,4,5} as a*b=a+b (mod 6). Show that zero is the identity for this operation and each element a of the set is invertible with 6-a being the inverse of adot OR A binary operation * on the set {0,1,2,3,4,5} is defined as a*b={a+b ,ifa+b<6a+b-6,ifa+bgeq6 Show that zero is the identity for this operation and each element a of set is invertible with 6-a , being the inverse of a.

Define a binary operation ** on the set {0, 1, 2, 3, 4, 5} as a**b={a+b if a+b<6; a+b-6,if a+b geq 6 . Show that zero is the identity for this operation and each element a !=0 of the set is invertible with 6-a being the inverse of a

Consider the binary operation ** on the set {1, 2, 3, 4, 5} defined by a ** b=min. {a, b} . Write the operation table of the operation ** .

A binary operation * on the set {0,1,2,3,4,5} is defined as: a * b={a+b ,a+b-6"\ \ \ \ if\ "a+b<6"\ \ \ if"\ a+bgeq6 Show that zero is the identity for this operation and each element a of the set is invertible with 6-a, being the inverse of a.

Consider the binary operation ^^ on the set {1, 2, 3, 4, 5} defined by a^^ b = " min "{a , b} . Write the operation table of the operation ^^ .

If the binary operation * on the set Z of integers is defined by a * b=a + b - 5 , then write the identity element for the operation * in Z.

Let **' be the binary operation on the set {1, 2, 3, 4, 5} defined by a**'b= HCF of a and b. Is the operation **' same as the operation ** defined Justify your answer.