Question

Find the value of its determinant ~


`\sf A = \begin{vmatrix} 1\: \: 2\: \: 1 \\ 2 \: \: 1 \: \: 2 \\ 1 \: \: 2 \: \: 1\end{vmatrix}`
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Answer 1

`\sf = \begin{vmatrix} 1\: \: 2\: \: 1 \\ \sf2 \: \: 1 \: \: 2 \\\sf 1 \: \: 2 \: \: 1\end{vmatrix} \\ \\ =\sf \begin{vmatrix} 1\: \: 2\\ \sf2 \: \: 1 \end{vmatrix} - 2 * \begin{vmatrix} 2\: \: 2\\ \sf 1 \: \: 1 \end{vmatrix} + \begin{vmatrix} 2\: \: \\\sf 1 \: \: 2 \end{vmatrix} \\ \\\sf \sf = ( 1 - 2 * 2) - 2(2 - 2) + (2 * 2 - 1) \\ \\ \sf= (1 - 4) - 2 * 0 + (4 - 1) \\ \\\sf = \cancel{ - 3} - 0 + \cancel3 \\ \\ \sf = 0`