[math-fun] Consequential zero entries in an orthogonal matrix

Counter-example? 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 Tom Fred Lunnon writes:

A denotes a 5x5 orthogonal matrix, with A_21 = A_31 = A_43 = A_53 = 0 ; why should necessarily A_13 = 0 also?

Generalise ... ??

WFL