Given the matrix \[k=\left( \begin{matrix} 2 & 1 \\ 3 & 4 \\\end{matrix} \right)\]the matrix ${{k}^{2}}+k+1$ is , where I is the 2× 2 identity matrix
\[\left( \begin{matrix} 7 & 2 \\ 12 & 21 \\\end{matrix} \right)\]
\[\left( \begin{matrix} 6 & 3 \\ 13 & 20 \\\end{matrix} \right)\]
\[\left( \begin{matrix} 9 & 8 \\ 22 & 23 \\\end{matrix} \right)\]
\[\left( \begin{matrix} 10 & 7 \\ 21 & 24 \\\end{matrix} \right)\]
\[\begin{align} & k=\left( \begin{matrix} 2 & 1 \\ 3 & 4 \\\end{matrix} \right) \\ & {{k}^{2}}=k\times k=\left( \begin{matrix} 2 & 1 \\ 3 & 4 \\\end{matrix} \right)\left( \begin{matrix} 2 & 1 \\ 3 & 4 \\\end{matrix} \right) \\ & {{k}^{2}}=\left( \begin{matrix} 2\times 2+1\times 3 & 2\times 1+1\times 4 \\ 3\times 2+4\times 3 & 3\times 1+4\times 4 \\\end{matrix} \right)=\left( \begin{matrix} 7 & 6 \\ 18 & 19 \\\end{matrix} \right) \\ & {{k}^{2}}+k+1=\left( \begin{matrix} 7 & 6 \\ 18 & 19 \\\end{matrix} \right)+\left( \begin{matrix} 2 & 1 \\ 3 & 4 \\\end{matrix} \right)+\left( \begin{matrix} 1 & 0 \\ 0 & 1 \\\end{matrix} \right)=\left( \begin{matrix} 10 & 7 \\ 21 & 24 \\\end{matrix} \right) \\\end{align}\]