GATE Chemical 2024 | Question: 20

Question

Consider a matrix $\text{A}=\left[\begin{array}{cc}-5 & a \\ -2 & -2\end{array}\right]$, where $a$ is a constant. If the eigenvalues of $\text{A}$ are $-1$ and $-6$, then the value of $a$, rounded off to the nearest integer, is $\_\_\_\_\_\_$.