Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2013 / Paper 2 / 12 / b / v

Repeatedly using the quadratic identity givesIn entries these are $(-1{)}^n{4}^{-n}\left(\begin{array}{cc}1& 0\\ 0& 1\end{array}\right)$ and $(-1{)}^n{2}^{-(2n+1)}\left(\begin{array}{cc}0& 1\\ -1& 0\end{array}\right)$, respectively. This is the basic reduction for functions of a two-dimensional antisymmetric matrix.