For any 2 × 2 matrix A, if $A

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Matrices

Question:

For any 2 × 2 matrix A, if $A (adj\, A) =\begin{bmatrix}10&0\\0&10\end{bmatrix}$, then $|A|$ is equal to

Options:

100

Correct Answer:

Explanation:

We know that for any square matrix A.

$A (adj\, A) = |A|I$

$∴A (adj\, A) =\begin{bmatrix}10&0\\0&10\end{bmatrix}=10I_2⇒|A|I_2=10I_2⇒|A|=10$