Q39Multiple correct2 Marks10 Jul 2022

Choose the correct options.

A

The row reduced echelon form of an $n\times n$ orthogonal matrix is the identity matrix of order $n$.

B

Suppose $A$ is a non-zero $n\times n$ matrix whose columns are mutually orthonormal in $\mathbb{R}^n$. Then $A^TA=I$.

C

The trace of an $n\times n$ orthogonal matrix is $0$.

D

Suppose $A$ is a non-zero $m\times n$ matrix whose columns are mutually orthogonal in $\mathbb{R}^m$. Then $AA^T$ is a diagonal matrix of order $m$.