Word Count : 351

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We are given a group \( G \) with the presentation \[ G = \langle a, b \mid a^2, b^3, aba^{-1}b^{-1} \rangle. \] This means: - \( a^2 = e \) (the identity element), - \( b^3 = e \), - The relation \( aba^{-1}b^{-1} = e \) (which is the commutator condition that \( a \) and \( b \) commute). We are tasked with showing that \( G \) is the cyclic group of order 6. ### Step 1: Interpret the relations 1. \( a^2 ________ ____ _________ ________ __________ ________ ____ _______ ____ ________.
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