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10 cards from this deck
Function taking 2 inputs from a set, output also in set (closure)
a∗b=b∗aa * b = b * aa∗b=b∗a for all elements in the set
(a∗b)∗c=a∗(b∗c)(a * b) * c = a * (b * c)(a∗b)∗c=a∗(b∗c) for all elements
Element eee where a∗e=e∗a=aa * e = e * a = aa∗e=e∗a=a for all aaa
Element a−1a^{-1}a−1 where a∗a−1=a−1∗a=ea * a^{-1} = a^{-1} * a = ea∗a−1=a−1∗a=e
Element where a−1=aa^{-1} = aa−1=a, so a∗a=ea * a = ea∗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
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