If A= \begin{bmatrix} p& 2\\ 2& p\end{bmatrix} and\: \left | A^{3} \right |= 125, then find the values of p.

 

 

 

 
 
 
 
 

Answers (1)

given A= \begin{bmatrix} p &2 \\ 2& p \end{bmatrix} and \left | A^{3} \right |= 125
          Now \left | A^{3} \right |= 125
                   \left | A^{3} \right |= 5^{3}
                  \left | A \right |= 5
Also we have \left | A \right |= \begin{bmatrix} p &2 \\ 2&p \end{bmatrix}
              \Rightarrow p^{2}-4= 5
              \Rightarrow p^{2}-9
              \Rightarrow p= \pm 3    

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