If $A.adjA =\begin{bmatrix}10&0\\0&10\end{bmatrix}$, then |A| is equal to
Answer & explanation
Correct answer: option 2
We know that $A^{-1}=\frac{adjA}{|A|}$ or, $I =\frac{A.adjA}{|A|}$
Here $A. adj A = \begin{bmatrix}10&0\\0&10\end{bmatrix}$ ⇒ A. adj A = 10 I .
⇒ |A| = 10.
Hence (B) is the correct answer.