Question

The determinant of a 3 × 3 matrix \( M \) is 8. If every element of \( M \) is multiplied by \( -2 \), the determinant of the modified matrix will be:

• A. −64
• B. −16
• C. 8
• D. 64

Hint:

When scaling all elements of a matrix by a constant \( k \), the determinant is scaled by \( k^n \), where \( n \) is the order of the matrix.

Answer 1

The Correct Option is A

Concept:
When every element of a matrix is multiplied by a constant \( k \), the determinant of the matrix is multiplied by \( k^n \), where \( n \) is the order (size) of the square matrix.

Given:
The matrix is of order \( 3 \times 3 \), and the original determinant is \( 8 \).
Each element is multiplied by \( -2 \).

Step-by-step Calculation:
Since it's a 3 × 3 matrix, the new determinant becomes: \[ \text{New Determinant} = (-2)^3 \times 8 = -8 \times 8 = -64 \]
✔️ Final Answer: The determinant of the modified matrix is \( -64 \).