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|\, = $
- A$0$
- ✓$10$
- C$20$
- D$100$
✓
Answer
Correct option: B.
$10$
b
(b) $A(adj\,.\,A) = |A|\,I \Rightarrow \,\left| {\,\begin{array}{*{20}{c}}{10}&0\\0&{10}\end{array}\,} \right| = 10\,.\,\left| {\,\begin{array}{*{20}{c}}1&0\\0&1\end{array}\,} \right|$.
(b) $A(adj\,.\,A) = |A|\,I \Rightarrow \,\left| {\,\begin{array}{*{20}{c}}{10}&0\\0&{10}\end{array}\,} \right| = 10\,.\,\left| {\,\begin{array}{*{20}{c}}1&0\\0&1\end{array}\,} \right|$.
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