Question

If $a,b,c,d\in G$, then${\left(abcd\right)}^{-1}=?$

Short answer

The inverse of${\left(abcd\right)}^{-1}$ is $d^{-1}{c}^{-1}{b}^{-1}{a}^{-1}$

Step-by-step solution

Inverse of an element

Let be a group. An element$a^{-1}\in G$ is said to be the inverse of an element $a\in G$if it satisfies$a\ast a^{-1}=a^{-1}\ast a=e$ , where$e\in G$ is the identity element.