Discussion
A 3 by 3 matrix has determinant 5. The determinant of twice that matrix is
Answer: C
Each of the three rows contributes one factor of \( k \), so for a matrix of order \( n \):
\[ \det(kA) = k^{n}\det A \]
\[ \det(2A) = 2^{3}\times 5 = 8 \times 5 = 40 \]
Using a single factor of two and reporting 10 is the classic error with this property.
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