Question:
If $B=\left[\begin{array}{ccc}5 & 2 \alpha & 1 \\ 0 & 2 & 1 \\ \alpha & 3 & -1\end{array}\right]$ is the inverse of a $3 \times 3$
matrix A, then the sum of all values of $\alpha$ for which det $(\mathrm{A})+1=0$, is :
Correct Option: , 3
Solution:
$|B|=5(-5)-2 \alpha(-\alpha)-2 \alpha$
$=2 \alpha^{2}-2 \alpha-25$
$1+|\mathrm{A}|=0$
$\alpha^{2}-\alpha-12=0$
Sum $=1$