If B = [ * 20 c 5& 2 &1 0&2&1 &3& - 1 ] is the inverse of a 3 3 m… - Vidyadip

MCQ

If $B = \left[ {\begin{array}{*{20}{c}}
5&{2\alpha }&1\\
0&2&1\\
\alpha &3&{ - 1}
\end{array}} \right]$ is the inverse of a $3 \times 3$ matrix $A$, then the sum of all values of $\alpha $ for which $det\, (A) + 1 = 0$, is

A
$0$
B
$-1$
✓
$1$
D
$2$

✓

Answer

Correct option: C.

$1$

c
$\left| B \right| = 5\left( { - 5} \right) - 2\alpha \left( { - \alpha } \right) - 2\alpha $

$ = 2{\alpha ^2} - 2\alpha - 25$

$1 + \left| A \right| = 0$

${\alpha ^2} - \alpha - 12 = 0$

Sum $=1$

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