Question

Consider the additive group${\mathbb{Z}}_2$ and the multiplicative group $\mathit{L}\mathbf{=}\mathbf{\{}\mathbf{\pm }\mathbf{1}\mathbf{,}\mathbf{\pm }\mathbf{i}\mathbf{\}}$ofcomplex numbers. Write out the operation table for the group${\mathit{\mathbb{Z}}}_{\mathbf{2}}\mathbf{\times }\mathit{L}$ .

Short answer

The operation table for the group is,

Step-by-step solution

Obtain operation table

Consider the given group,

The additive group ${\mathbb{Z}}_2$and multiplicative group$L=\{\pm 1,\pm i\}$ .

Determine operation table

Obtaining operation table for the group ${\mathbb{Z}}_2\times L$.

The operation table is,