[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#