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A matrix A is called orthonormal if AAT = I. (a) Show that an orthonormal matrix...

A matrix A is called orthonormal if AAT = I. (a) Show that an orthonormal matrix is invertible and that the inverse is orthonormal. (b) Showtheproductoftwoorthonormalmatricesisalsoorthonormal. (c) By trials and errors, nd three orthonormal matrices of order 2. (d) Let x be a real number, show that the matrices A =cosx −sinx sinx cosx, B = cosx sinx −sinx cosx are orthonormal.

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