If \( A=\left[\begin{array}{lll}0 & 1 & 0 \\ 0 & 0 & 1 \\ p & q & r...

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If \( A=\left[\begin{array}{lll}0 & 1 & 0 \\ 0 & 0 & 1 \\ p & q & r\end{array}\right] \) and \( I \) is the identity matrix of order 3 , show that \( A^{3}=p I+q A+r A^{2} \).
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