# Similar matrices

Show that if A and B are similar matrices, then the det(A)=det(b).

I am not entirely sure how to start this proof.
I was thinking...
A=ai j

det(A)=$$\sum$$ai j*(-1)i+j*Mi j from j=1 to n.

I am pretty much clueless on this one though and not sure if I am just throwing stuff on the wall hoping something will stick

Related Calculus and Beyond Homework Help News on Phys.org
marcusl
Gold Member
Write down the definition of similar matrices. What do you know about determinants that you can apply to that equation?

Matrix A is similar to B if there exists S such that B=S-1*A*S

det(B)=det(S-1*A*S)=det(S-1)det(A)det(S)=det(S-1*S)det(A)=det(I)det(A)=det(A) thus, det(B)=det(A)

Remarkable easy.

marcusl