Question

If \( A \) is a non-singular matrix of order 3 and \( |A| = 2 \), then \( |\text{adj}(A)| \) equals:

• A. 4
• B. 6
• C. 8
• D. None of these

Hint:

For a matrix \( A \) of order \( n \), \( |\text{adj}(A)| = |A|^{n-1} \). This property is useful when calculating the determinant of the adjugate matrix.

Answer 1

The Correct Option is A

Step 1: Using the property of adjugate matrix.
For a square matrix \( A \) of order \( n \), the determinant of the adjugate matrix \( \text{adj}(A) \) is given by: \[ |\text{adj}(A)| = |A|^{n-1} \] For \( A \) of order 3, we have \( n = 3 \), and thus: \[ |\text{adj}(A)| = |A|^{3-1} = |A|^2 \] Step 2: Substituting the value of \( |A| \).
We are given that \( |A| = 2 \), so: \[ |\text{adj}(A)| = 2^2 = 4 \] Step 3: Conclusion.
Thus, \( |\text{adj}(A)| = 4 \), corresponding to option (a).