If P is a 3×3 matrix such that P’ = 2P + I, where P’ is the transpose of P, then: 

Given: ${\mathrm{P}}^{\mathrm{\prime }}=2P+I$      ...(i)
Therefore, ${\left(P^{\mathrm{\prime }}\right)}^{\mathrm{\prime }}=(2P+I{)}^{\mathrm{\prime }}$
$\begin{array}{l}\text{ i.e. }\mathrm{P}=2{\mathrm{P}}^{\mathrm{\prime }}+\mathrm{I}\\ \text{ i.e. }\mathrm{P}=2(2\mathrm{P}+\mathrm{I})+\mathrm{I} ....\mathrm{From} \left(\mathrm{i}\right)\\ \Rightarrow 3P=-3I\\ \Rightarrow P=-I\end{array}$
Therefore, P=-I