Question

Find the order of the given element.

(c) $\left(\begin{array}{cc}-\frac{1}{2}& \frac{1}{2}\\ -\frac{3}{2}& \frac{1}{2}\end{array}\right)$in$\mathit{G}\mathit{L}\mathbf{(}\mathbf{2}\mathbf{,}\mathbf{}\mathit{R}\mathbf{)}$

Short answer

The order of $\left(\begin{array}{cc}-\frac{1}{2}& \frac{1}{2}\\ -\frac{3}{2}& \frac{1}{2}\end{array}\right)$in $GL(2,R)$is $3$.

Step-by-step solution

GL(2, R)

The group $\mathit{G}\mathit{L}\mathbf{(}\mathbf{}\mathbf{2}\mathbf{,}\mathbf{}\mathit{R}\mathbf{)}$ is a group of all $\mathbf{2}\mathbf{\times }\mathbf{2}$invertible matrices over the field of real numbers $\mathit{R}$

Find the order of the given element.

Find the order of the given element.