[NBHM_2006_PhD Screening Test 2006_Algebra]
Let $A$ be an $3\times 3$ orthogonal matrices with real entries,Then which are true
$\det A$ is rational number
$d(Ax,Ay)=d(x,y)$ for any two vector $x,y\in \mathbb{R}^3$ where $d$ is ussual eucledean distance.
All entries off $A$ are positive.
All eigen values of $A$ are real.
determinant of orthogonal matrix is $\{1,-1\}$ so 1 is true, modulas of eigen values of an orthogonal matrix is $1$ so 4 may not be true always, I am not getting anything about 2 and 3. Thank you.