Question was
Let $$A= \left[\begin{matrix} a_1 & a_2\\ a_3&a_4\\ \end{matrix}\right]$$ $$P= \left[\begin{matrix} p_1 & p_2\\ p_3&p_4\\ \end{matrix}\right]$$
Find the matrix $Q$ such that
$$ Q\left[ \begin{array} \\ p_1\\p_3\\p_2\\p_4 \end{array} \right] = \left[ \begin{array} \\ 1\\0\\0\\1 \end{array} \right]$$ is equivalent to the equation $A^TPA+P=I$
In this question I approached to make $Q$ to $2\times 2$ matrix. but I couldn't get any idea.. I need you genius to help.