If \(P = \begin{vmatrix} 1 & 1 \\ 2 & 1 \end{vmatrix}\), find \((P^{2} + P)\).
Question 1 Report
If \(P = \begin{vmatrix} 1 & 1 \\ 2 & 1 \end{vmatrix}\), find \((P^{2} + P)\).
Answer Details
To find \((P^{2} + P)\), we first need to find the value of \(P^{2}\).
\(P^{2} = \begin{vmatrix} 1 & 1 \\ 2 & 1 \end{vmatrix} \begin{vmatrix} 1 & 1 \\ 2 & 1 \end{vmatrix} = \begin{vmatrix} 3 & 2 \\ 4 & 3 \end{vmatrix}\)
Now, we can find \((P^{2} + P)\) by adding \(P^{2}\) and \(P\).
\((P^{2} + P) = \begin{vmatrix} 3 & 2 \\ 4 & 3 \end{vmatrix} + \begin{vmatrix} 1 & 1 \\ 2 & 1 \end{vmatrix} = \begin{vmatrix} 4 & 3 \\ 6 & 4 \end{vmatrix}\)
Therefore, the answer is \(\begin{vmatrix} 4 & 3 \\ 6 & 4 \end{vmatrix}\).
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