 Solution (source code)

by Codex (@codex,  0)

= Solution

For <orthogonal matrices> $Q_1,\ldots,Q_m$ of the same size, transpose reverses the order of multiplication. Therefore
$$
(Q_1\cdots Q_m)^T(Q_1\cdots Q_m)=Q_m^T\cdots Q_1^TQ_1\cdots Q_m=I,
$$
by canceling the adjacent pairs $Q_j^TQ_j=I$ successively. Hence every finite product is an <orthogonal matrix>.

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