Eigenvalues & eigenvectors of a specific product of three matrices How is possible, without multiplying, find the eigenvalues and eigenvectors of the A matrix ? 
Which propriety should I use?
$$A=
\begin{pmatrix} \cos \theta & -\sin \theta\\
\sin \theta & \cos \theta \end{pmatrix}
\begin{pmatrix} 3 & 0\\
0 & 7 \end{pmatrix}
\begin{pmatrix} \cos \theta & \sin \theta\\
-\sin \theta & \cos \theta \end{pmatrix}$$

You have $A = R_\theta \Lambda R_{-\theta}$, where $R_t$ is a rotation by an angle $t$. We see that $R_\theta  R_{-\theta} = I$, so they are inverses, and
so the eigenvalues of $A$ and $\Lambda$ will be the same. 
If $\Lambda$ is diagonal, it is easy to read off the eigenvalues.
