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

[asdf1]

why does det(kA)=(k^n)detA and not kdetA?

 

[Meir Achuz]

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).

 

[asdf1]

thank you very much!