If $A.adjA =\begin{bmatrix}10&0\\0&a

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Matrices

Question:

If $A.adjA =\begin{bmatrix}10&0\\0&10\end{bmatrix}$, then |A| is equal to

Options:

100

none of these

Correct Answer:

Explanation:

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.