Question:
Write the value of the determinant $\left|\begin{array}{cc}p & p+1 \\ p-1 & p\end{array}\right|$.
Solution:
$\left|\begin{array}{cc}p & p+1 \\ p-1 & p\end{array}\right|=p^{2}-(p+1)(p-1)$
$=p^{2}-\left(p^{2}-1\right)$
$=p^{2}-p^{2}+1$
$=1$
Hence, the value of the determinant $\left|\begin{array}{cc}p & p+1 \\ p-1 & p\end{array}\right|$ is 1 .
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