Largest eigenvalue after squaring

For $A = \begin{pmatrix} 0 & 2 \\ 1 & -1 \end{pmatrix}$ , let $B = A^2$ . What is the largest eigenvalue of $B$ ?

Show hints (2)+

Find both eigenvalues of $A$ from $\lambda^2 - (\mathrm{tr})\lambda + \det = 0$ : they are $1$ and $-2$ .
Eigenvalues of $A^2$ are the squares $\{1, 4\}$ - the largest ( $4$ ) comes from $-2$ .

Answer

Reveal answer →

Want the full step-by-step worked solution? It's part of Premium - along with a worked solution for every question in the bank.

Asked at: Probability & Market-Making, Data-Driven Research