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Problem If a \mathbf{a} a b \mathbf{b} b c \mathbf{c} c a − 1 \mathbf{a}^{-1} a − 1 b − 1 \mathbf{b}^{-1} b − 1 c − 1 \mathbf{c}^{-1} c − 1 [ a b c ] ≠ 0 [\mathbf{abc}] \neq 0 [ abc ] = 0 [ a − 1 b − 1 c − 1 ] [\mathbf{a}^{-1} \mathbf{b}^{-1} \mathbf{c}^{-1}] [ a − 1 b − 1 c − 1 ] [ a b c ] [\mathbf{abc}] [ abc ] Browse the problem library