If every element of an n x n square matrix A is multiplied by a non-zero scalar k, what is the determinant of kA?
Answer and explanation
Correct answer: C. k^n det A
- Step 1: Factoring out scalar k from each of the n rows yields k^n. Step 2. Therefore, det(kA) = k^n det(A). Answer: k^n det A. Why not the others: k det A applies only when multiplying a single row; n k det A assumes linear scaling; k^(n-1) omits one dimension factor.
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