Question-5

Find the determinant of the following matrix:

\[ \begin{bmatrix}1 & 0 & 1 & 0\\ 0 & 1 & 0 & 1\\ 1 & 0 & 0 & 1\\ 0 & 0 & 0 & 1 \end{bmatrix} \]

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We can expand the determinant along the last row. The determinant of the entire matrix becomes the determinant of the following sub-matrix:

\[ \begin{bmatrix}1 & 0 & 1\\ 0 & 1 & 0\\ 1 & 0 & 0 \end{bmatrix} \]

We can expand this determinant again along the last row, which gives the result \(-1\).