Why Does det(kA) Equal (k^n)detA Instead of kdetA?

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The determinant of a scalar multiplied by a matrix, expressed as det(kA), equals k^n * det(A) for an n x n matrix A. This relationship arises because each term in the determinant calculation includes n factors, leading to the scalar k being multiplied n times. Thus, the correct formula is det(kA) = k^n * det(A), confirming the mathematical principle behind determinants and scalar multiplication.

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why does det(kA)=(k^n)detA and not kdetA?
 
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The matrlix kA has a factor of k in every element. Each term in the determinant of an nXn matrix has n factors, so k comes in n times.
Therefore, det(kA)=k^n det(A).
 
thank you very much!
 

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