1. The set {0,1} with the binary operation multiplication does not form a group.
The closure property is satisfied since 0*0 = 0, 0*1 = 1*0 = 0 and 1*1 = 1.
The associative property is satisfied (since multiplication is
associative).
The element 1 is the identity since 1*a = a = a*1 for each value a in
the set {0,1}.
But the element 0 has no inverse. There is no element a such that 0*a
= 1 (the identity).