Show that in 2D, the general orthogonal transformation as matrix A given by {{cos, sin}, {-sin,...

Show that in 2D, the general orthogonal transformation as matrix A given by

{{cos, sin}, {-sin, cos}}. Verify that det[A] = 1 and that the transpose of A equals its inverse. Let Tij be a tensor in this space. Write down in full the transformation equations for all its components and deduce that Tii is an invariant.

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