Any rotation of axes in three dimensions can be described by giving the nine direction cosines of the angle between the $\left(x,y,z\right)$axes and the $\left(x\text{'},y\text{'},z\text{'}\right)$axes. Show that the matrix A of these direction cosines in $\left(2.7\right)$or $\left(2.10\right)$is an orthogonal matrix. Hint: See Chapter 3, Section 9. Find $\mathit{A}{\mathit{A}}^{\mathbf{T}}$and use Problem 3.

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