Prove that if (mathbf{X}) is an (n times p) data matrix, then (operatorname{dVar}_{n}(a+) (b mathbf{X} C)=|b| operatorname{dar}_{n}(mathbf{X})),

Question:

Prove that if $\mathbf{X}$ is an $n \times p$ data matrix, then $\operatorname{dVar}_{n}(a+$ $b \mathbf{X} C)=|b| \operatorname{dar}_{n}(\mathbf{X})$, for all constant vectors $a$ in $\mathbb{R}^{p}$, scalars $b$, and $p \times p$ orthonormal matrices $C$.

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