Question

If $A$ is an orthogonal matrix and $B=AB,$ then $B^{T}A\left(B^T\text{is transpose of}B\right)$ is

• A. $A$
• B. $B$
• C. $A^T$
• D. $B^T$

Answer 1

The correct option is D $B^T$

Given : $A{A}^T=I=A^{T}A$
and $B=AB$
$\Rightarrow B^T=B^T{A}^T$
$\Rightarrow B^{T}A=B^T{A}^{T}A=B^T$