What is the relationship between det(A)\det(A)det(A) and det(Ak)\det(A^k)det(Ak) for a square matrix AAA?
det(Ak)=k⋅det(A)\det(A^k) = k \cdot \det(A)det(Ak)=k⋅det(A)
det(Ak)=(det(A))k\det(A^k) = (\det(A))^kdet(Ak)=(det(A))k
det(Ak)=det(A)+k\det(A^k) = \det(A) + kdet(Ak)=det(A)+k
det(Ak)=kndet(A)\det(A^k) = k^n \det(A)det(Ak)=kndet(A)