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NIMCET 2009 — Mathematics PYQ

NIMCET | Mathematics | 2009

If $A$ is a $3 \times 3$ matrix with $\det(A) = 3$ , then $\det(\text{adj } A)$ is:

Choose the correct answer:

Correct Answer:

9

Explanation

1. Identify the Given Information

Order of the matrix ( $n$ ) = $3$
Determinant of matrix $A$ , denoted as $|A|$ or $\det(A)$ = $3$

2. State the Relevant Property

There is a fundamental property in linear algebra that relates the determinant of the adjoint of a matrix to the determinant of the matrix itself:

\det(\text{adj } A) = (\det A)^{n-1}

where $n$ is the order of the square matrix $A$ .

3. Substitute the Values

By substituting the given values into the formula:

$n = 3$
$\det A = 3$

We get:

\det(\text{adj } A) = (3)^{3-1}

\det(\text{adj } A) = 3^2

\det(\text{adj } A) = 9

Conclusion:

The determinant of the adjoint matrix is $9$ .

Final Answer:

The correct option is (b) 9.