Question

Show that the determinant and trace of Matrix remains invariant under similarity transformation

Answer 1

\[
det( A^{-1} B A) =det(A^{-1}) det(B) det(A)=\frac 1 {det(A)}det(B) det (A) =det(B)

\]
Can you do the trace?

Answer 2

Use that trace(MN)=trace(NM)

Answer 3

\[
trace(A^{-1} B A)=trace( A^{-1} A B)=trace(B)
\]

Answer 4

thanks ... prof