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=ab(mod5). 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={1,2,3,4} as a*b=ab(mod5) 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 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 a . OR A binary operation ** on the set {0,1,2,3,4,5} is defined as a**b={[a+b if a+b = 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 a .

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 6a, 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.

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 is defined by a a^(*)b=a+b-5, then find the identity element with respect to *

Consider the infimum binary operation ^^ on the set S={1,2,3,4,5} defined by a^^b= Minimum of aandb .Write the composition table of the operation ^^ .