Question: Let T : R n R n be a linear transformation that preserves lengths; that is, T(x) = x for all x in R

Let T : Rn → Rn be a linear transformation that preserves lengths; that is, ΙΙT(x)ΙΙ = ΙxΙΙ  for all x in Rn.

a. Show that T also preserves orthogonality; that is, T(x) · T(y) = 0 whenever x · y = 0.

b. Show that the standard matrix of T is an orthogonal matrix.

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