if $\det(A) = 2$, what is $\det(A^3)$?

Question

What is the relationship between a determinant and the determinant of the same thing but to a power? Thank you.

https://math.stackexchange.com/questions/60284/how-to-show-that-detab-deta-detb — Ahmed S. Attaalla, Oct 18 '17 at 20:16
Determinant is a multiplicative function on square matrices of the same dimension. — Bernard, Oct 18 '17 at 20:16

score 5 · Answer 1 · answered Oct 18 '17 at 20:16

5

Since $\det(AB)=\det(A)\det(B)$, we obtain: $$\det(A^3)=(\det(A))^3=8$$

answered Oct 18 '17 at 20:16

Michael Rozenberg

1 Answers1