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STD 12 - 3 and 4 . determinant and metrices — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 3 and 4 . determinant and metrices4 Marks
Question
For any $2 \times 2$ matrix A, if $A(adj\,A) = \left[ {\begin{array}{*{20}{c}}{10}&0\\0&{10}\end{array}} \right]$ then $|A|$ is equal
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Answer

b
(b) We have, $A(adj\,A) = \left[ {\begin{array}{*{20}{c}}{10}&0\\0&{10}\end{array}} \right]$

or $A(adj\,A) = 10\,\left[ {\begin{array}{*{20}{c}}1&0\\0&1\end{array}} \right] = 10I$ …..(i)

and ${A^{ - 1}} = \frac{1}{{|A|}}\,(adj\,A)$

$A(adj\,A) = |A|\,I$…..(ii)

$\therefore $ From equation $(i) $ and $(ii)$, we get $|A| = 10$.

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