Q28Multiple correct4 Marks24 Mar 2024

Choose the correct options from the following.

A

If $A$ and $B$ are orthogonal matrices, then $AB$ is also orthogonal.

B

If $A$ is orthogonal, then $A^{-1}$ is also an orthogonal matrix.

C

Let $A$ be an $n\times n$ orthogonal matrix. Let $R$ be the set of rows of $A$ and $C$ be the set of columns of $A$. Then exactly one of $R$ or $C$ is an orthogonal subset of vectors.

D

If $A$ is an $n\times n$ orthogonal matrix, then $\lVert Ax\rVert=\lVert x\rVert$ for any $x\in\mathbb{R}^n$.