Question

Value of the determinant of a matrix \( A \) of order \( 3 \times 3 \) is 7Then the value of the determinant formed by the cofactors of matrix \( A \) is

• A. 7
• B. 49
• C. 14
• D. 343

Hint:

For an \( n \times n \) matrix, determinant of cofactor matrix is \( (\det A)^{n-1} \)Very important shortcut in matrices.

Answer 1

The Correct Option is B

Step 1: Recall cofactor matrix property.
If \( A \) is an \( n \times n \) matrix, then:
\[ \det(\text{cofactor matrix}) = (\det A)^{n-1} \]

Step 2: Substitute given values.
\[ n = 3,\quad \det A = 7 \]

Step 3: Apply formula.
\[ \det(\text{cofactor matrix}) = 7^{3-1} \]
\[ = 7^2 \]

Step 4: Compute value.
\[ 7^2 = 49 \]

Step 5: Match with options.
Correct option is (B).

Step 6: Interpretation.
Cofactor matrix determinant grows as power of original determinant.

Step 7: Final conclusion.
\[ \boxed{49} \]