How to construct a $2\times 2$ real matrix $A$ not equal to Identity such that $A^3=I$?
There is a correspondence between the ring of complex numbers and the ring of $2\times2$ matrices (0 matrix is included!) i.e.,$a+ib\leftrightarrow\begin{pmatrix}a&-b\\b&a\end{pmatrix}$
Can I apply this result and construct such matrix?