Evaluate | cc x & x+1 x-1 & x | - Vidyadip

Question

Evaluate $\left|\begin{array}{cc} {x} & {x+1} \\ {x-1} & {x} \end{array}\right|$

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Answer

We have $\left|\begin{array}{cc} {x} & {x+1} \\ {x-1} & {x} \end{array}\right|$ $= x (x) – (x + 1) (x – 1) = x^2 – (x^2 – 1) = x^2 – x^2 + 1 = 1$

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