Discrete Mathematics - Group Theory

A = {0, 1, 2, 3, ...} is the set of non-negative integers. Let F be the set of functions from A to itself. For any two functions, f1, f2 ∈ F, we define (f1⨀f2)(n) = f1(n) + f2(n) for every number n in A. Which of the fol...

Let Zₙ be the group of integers {0, 1, 2, ..., n-1} with addition modulo n as the group operation. The number of elements in the group Z₂ × Z₃ × Z₄ that are their own inverses is _________