Question

Prove that [ − sin sin cos ] is orthogonal.​

Answer 1

Answer:

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Answer 2

Answer:

nonsingular matrix is called orthogonal when its inverse is equal to its transpose:

AT=A−1→ATA=I.

For example, for the matrix

A=(cosθsinθ−sinθcosθ),

the inverse is

A−1=(cosθ−sinθsinθcosθ)=ATWe do not need to calculate the inverse to see if the matrix is orthogonal. We can transpose the matrix, multiply the result by the matrix, and see if we get the identity matrix as a result:

AT=(cosθ−sinθsinθcosθ)

ATA=(cosθ−sinθsinθcosθ)(cosθsinθ−sinθcosθ)=((cos2θ+sin2θ)00(sin2θ+cos2θ))=(1001)