Question

If \( A \) is a non-singular 3x3 matrix, then \( \left| 5A \right| \) is

• A. 25
• B. 5
• C. 64
• D. 125

Hint:

When multiplying a matrix by a scalar, the determinant is multiplied by the scalar raised to the power of the matrix's order.

Answer 1

The Correct Option is D

The determinant of a matrix is scaled by the factor of the scalar raised to the power of the size of the matrix. That is, for a matrix \( A \), and a scalar \( k \), \[ |kA| = k^n |A|, \] where \( n \) is the order of the matrix. In this case, \( n = 3 \), so: \[ |5A| = 5^3 |A| = 125 |A|. \]