Question: If $A = \begin{bmatrix} \alpha & 2 \\ 2 & \alpha \end{bmatrix}$and $|A^{3}| = 125$then \(\alpha\...

Question

If $A = \begin{bmatrix} \alpha & 2 \\ 2 & \alpha \end{bmatrix}$ and $|A^{3}| = 125$ then $\alpha$ =

Answer 1

$125 = |A^{3}| = |A|^{3} \Rightarrow |A| = 5$ and $|A| = \alpha^{2} - 4 = 5$ ⇒ $\alpha^{2} = 9$

⇒ $\alpha = \pm 3$

Question: If \(A = \begin{bmatrix} \alpha & 2 \\ 2 & \alpha \end{bmatrix}\)and \(|A^{3}| = 125\)then \(\alpha\...