For any 2 2 matrix A, if A(adj ,A) = [ * 20 c 10 &0 0& 10 ] then … - Vidyadip

MCQ

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

A
$0$
✓
$10$
C
$20$
D
$100$

✓

Answer

Correct option: B.

$10$

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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