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Determinants

Example 2 Evaluate $|\begin{smallmatrix}x&x+1\\ x-1&x\end{smallmatrix}|$

Solution

We have \(|\begin{smallmatrix}x&x+1\\ x-1&x\end{smallmatrix}|=x(x)-(x+1)(x-1)=x^{2}-(x^{2}-1)=x^{2}-x^{2}+1=1\)