Consider the group presentation

$(a^2{b}^2{c}^2,a^{-1}b{c}^{-1},ab{a}^{-1}{b}^{-1}$:$|)$

Show that, modulo the relations, we have

$b{a}^{2}c{b}^{-1}ab{c}^2=e.$

Show all steps. $($Hint: Try inserting $a^{-1}b{c}^{-1}$ between some letters and see how this goes. Also, note that the relation $ab{a}^{-1}{b}^{-1}$ tells us that $ab=ba,$ it can be very useful!$)$