Binary Operations (AQA A-Level Further Maths): Flashcards

Function taking 2 inputs from a set, output also in set (closure)

$a * b = b * a$ for all elements in the set

$(a * b) * c = a * (b * c)$ for all elements

Element $e$ where $a * e = e * a = a$ for all $a$

Element $a^{-1}$ where $a * a^{-1} = a^{-1} * a = e$

Element where $a^{-1} = a$, so $a * a = e$

Grid showing results of binary operation on all pairs of elements

Column identical to initial column; element at top is identity

Symmetry along main diagonal indicates commutative operation

Always unique for any binary operation