Chapter 6, Problem 47E

If A and B are orthogonal $n\times n$ matrices such that $\det A=\det B=1$ , then matrices A and B must commute.
_________________________________
¹²The even integers are $0,\pm 2,\pm 4,\mathrm{...},$ while the odd integersare $\pm 1,\pm 3,\mathrm{...}$