JEE Main 2026 (Online) 23rd January Evening ShiftQuestion 1
Let $A=\begin{bmatrix}0&2&-3\\-2&0&1\\3&-1&0\end{bmatrix}$ and $B$ be a matrix such that $B(I-A)=I+A$. Then the sum of the diagonal elements of $B^TB$ is equal to $\_\_\_\_\_\_$ .
Matrices
Answer$3$
Solution
$B=(I+A)(I-A)^{-1}$ with $A$ skew-symmetric, so $B$ is orthogonal: $B^TB=I$ and the trace is $3$.