Why does $\det(A^2)= \det(A)^2$?

Asked Dec 11 '16 at 04:44

Active Dec 11 '16 at 12:15

Viewed 172 times

Question in Title. Why does $\det(A^2)=\det(A)^2$? Old quiz answers gave this as a proof of why if matrix $A=A^2$, then $A=0$ or $1$.

edited Dec 11 '16 at 12:15

Martin Sleziak

asked Dec 11 '16 at 04:44

8

Hint: What is $\det AB$? See: http://math.stackexchange.com/questions/60284/how-to-show-that-detab-deta-detb and http://www.math.lsa.umich.edu/~speyer/417/DetMult.pdf – Moo Dec 11 '16 at 04:45
The determinant of a matrix is the factor by which the volume of any region is increased by the linear transformation represented by the matrix. – WW1 Dec 11 '16 at 05:20

0 Answers0