Let [A = | pmatrix 5 & 5 & 0 & & 5 0 & 0 & 5 pmatrix |.] If [,,| A^2 | = 25,] then [,| |] …

Question

Let $$A = \left| {\begin{pmatrix} 5 & {5\alpha } & \alpha   \
   0 & \alpha  & {5\alpha }  \
   0 & 0 & 5  \ \end{pmatrix} } \right|.$$ If $$\,\,\left| {{A^2}} \right| = 25,$$ then $$\,\left| \alpha  \right|$$ equals

Accepted Answer

$$\left| {{A^2}} \right| = 25 \Rightarrow {\left| A \right|^2} = 25$$

$$ \Rightarrow {\left( {25\alpha } \right)^2} = 25 \Rightarrow \left| \alpha  \right| = {1 \over 5}$$

Solutions · 1