Question

Let \( A \) be a square matrix of order 3x3. Then \( |2A| \) is equal to:

• A. \( 2|A| \)
• B. \( 4|A| \)
• C. \( 8|A| \)
• D. None of these

Hint:

When multiplying a matrix by a scalar, the determinant is multiplied by the scalar raised to the power of the order of the matrix: \( |kA| = k^n |A| \).

Answer 1

The Correct Option is B

Step 1: Using the property of determinants.
For a square matrix \( A \) of order \( n \), if \( A \) is multiplied by a scalar \( k \), then: \[ |kA| = k^n |A| \] where \( n \) is the order of the matrix. Step 2: Applying this to the given matrix.
Since \( A \) is a 3x3 matrix, we have \( n = 3 \), and the scalar is 2. Thus: \[ |2A| = 2^3 |A| = 8 |A| \] Step 3: Conclusion.
Thus, \( |2A| = 8|A| \), corresponding to option (c).