NIMCET 2009 — Mathematics PYQ

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:

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:

Conclusion:

The determinant of the adjoint matrix is $9$.

Final Answer:

The correct option is (b) 9.