Let A = ( * 20 c 1& - 1 &1 2&1& - 3 1&1&1 ) and (10)B = ( * 20 c … - Vidyadip

MCQ

Let $A = \left( {\begin{array}{*{20}{c}}1&{ - 1}&1\\2&1&{ - 3}\\1&1&1\end{array}} \right)$ and $(10)B = \left( {\begin{array}{*{20}{c}}4&2&2\\{ - 5}&0&\alpha \\1&{ - 2}&3\end{array}} \right)$. If $B$ is the inverse of matrix $A$, then $\alpha $ is

✓
$5$
B
$-1$
C
$2$
D
$-2$

✓

Answer

Correct option: A.

$5$

a
(a) Given, $\left( {\begin{array}{*{20}{c}}4&2&2\\{ - 5}&0&\alpha \\1&{ - 2}&3\end{array}} \right)\, = \,10{A^{ - 1}}$

$ \Rightarrow $ $\left( {\begin{array}{*{20}{c}}4&2&2\\{ - 5}&0&\alpha \\1&{ - 2}&3\end{array}} \right)\,\,\left( {\begin{array}{*{20}{c}}1&{ - 1}&1\\2&1&{ - 3}\\1&1&1\end{array}} \right) = \left( {\begin{array}{*{20}{c}}{10}&0&0\\0&{10}&0\\0&0&{10}\end{array}} \right)$

$ \Rightarrow $ $ - 5 + \alpha = 0 \Rightarrow \alpha = 5$

(Equating the element of $2nd$ row and first column).

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