A is a rotation matrix by angle θ. Two rotations of θ compose to a rotation of 2θ. Direct multiplication confirms each entry uses the double-angle identities, giving cos2θ and sin2θ in place of cosθ and sinθ.
If the matrix A=[cosθ−sinθsinθcosθ], then A2 is equal to:
Held on 25 May 2023 · Verified 13 Jul 2026.
[cos2θ−sin2θsin2θcos2θ]
[cos2θ−sin2θsin2θcos2θ]
[cosθ2−sinθ2sinθ2cosθ2]
[cosθ+sinθsinθ−cosθcosθ−sinθcosθ+sinθ]
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