JEE Main 2024 (Online) 1st February Morning ShiftQuestion 1
If $A=\begin{bmatrix}\sqrt{2}&1\\-1&\sqrt{2}\end{bmatrix}$, $B=\begin{bmatrix}1&0\\1&1\end{bmatrix}$, $C=ABA^{T}$ and $X=A^{T}C^{2}A$, then $\det X$ is equal to :
Determinant
Solution
$|A|=2+1=3$, $|B|=1$, $C=ABA^T\Rightarrow|C|=9$. $|X|=|A^T||C|^2|A|=3\cdot81\cdot3=729$. Option B.