Question

Find the order of the given element.

in

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 $GL\left(2\mathrm{ℝ}\right)$is $3$.

Step-by-step solution

GL(2ℝ)

The group is a group of all invertible matrices over the field of real numbers

 Order of an element

Order of an element is defined as a positive integer n such that , where is the identity element in