Question

If \( A \) is a square matrix of order 2 such that \( \text{det} = 4 \), then \( \text{det}(4 \, \text{adj} \, A) \) is equal to:

• A. 16
• B. 64
• C. 256
• D. 512

Hint:

For matrix adjoints, the determinant of the adjoint of a matrix is related to the determinant of the original matrix by \( \text{det}(\text{adj}) = (\text{det})^{n-1} \) for an \( n \times n \) matrix.

Answer 1

The Correct Option is B

For a 2x2 matrix \( A \), the determinant of \( k \) times the adjugate matrix is \( \text{det}(k \, \text{adj}) = k^2 \cdot \text{det} \).
Given that \( \text{det} = 4 \), \[\text{det}(4 \, \text{adj} \, A) = 4^2 \cdot 4 = 16 \cdot 4 = 64.\]