[MATRICES] Determine a so it meets the condition? Thank you!

Question

$((cos x,-sin x),(sin x,cos x))$ ³ =

$((cos(a * x),sin(a * x)),(-sin(a * x),cos(a * x)))$ ^-1

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Answer 1 · 2017-12-15T23:00:09

$a=3$

Calling $R(x) = ((cos x,-sin x),(sin x,cos x))$

$R(x)$ as defined is a rotation matrix so one of it's properties is

$R(x)^n = R(nx)$

also $R(x)^top = R(x)^-1 = R(-x)$

so we have

$R(x)^3 = R(3x) = (R(ax)^top)^-1 = R(ax)$ so we conclude that

$a=3$