Question

Eigen values of a matrix $S=\left[\begin{array}{cc}3& 2\\ -2& 3\end{array}\right]$ are $5$ and $1$. What are the eigenvalues of the matrix $S^2=SS$ ?

• A. $1$ and $25$
• B. $6$ and $4$
• C. $5$ and $1$
• D. $2$ and $1$

Answer 1

The correct option is A $1$ and $25$

If $\lambda$ is an eigen value of matrix $A$ then the eigen value of $A^n$ is ${\lambda }^n,nϵN$.