Exercise 3.3.6

Question

Prove that if $A$ and $B$ are similar, then $\det A = \det B$.

Jing Huang · Accepted Answer

\begin{proof}
$A$ and $B$ are similar, then $A = Q^{-1} B Q$ for an invertible matrix $Q$. Then
%%%%%%%%%%%%%%%%%
\begin{equation*}
    \begin{split}
    \det A &= \det Q^{-1} B Q   \
           &= (\det Q^{-1}) (\det B) (\det Q) \
           &= (\det Q^{-1}) (\det Q) (\det B) \
           &= (\det Q^{-1} Q) (\det B) \
           &= (\det I) (\det B)  \
           &= \det B.
    \end{split}
\end{equation*}
%%%%%%%%%%%%%%%%%
\end{proof}

Exercise 3.3.6

Answers

Comments

Exercise 3.3.6

Answers

Comments

Add answer