JEE Main 2016 (Offline)Question 1
If $A=\begin{bmatrix}5a&-b\\3&2\end{bmatrix}$ and $A\cdot\operatorname{adj}A=AA^{T}$, then $5a+b$ is equal to
Matrices
Solution
$A\operatorname{adj}A=|A|I=AA^T$ gives off-diagonal $15a-2b=0$ and $13=|A|=10a+3b$. So $a=\frac25$, $b=3$, and $5a+b=5$.