Abstract Algebra: Theory and Applications · Problem 14

Permutation Groups — Thomas Judson

Mathematics — Abstract Algebra · cyclic-groups-finite-order

Problem

Let

A = \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix} \quad \text{and} \quad B = \begin{pmatrix} 0 & -1 \\ 1 & -1 \end{pmatrix}

be elements in

GL_2(\mathbb{R})

. Show that

A

and

B

have finite orders but

AB

does not.