If $f(x) = \begin{vmatrix}0&x-1&x-2\\x+1&0&x-3\\x + 2&x +3&0\end{vmatrix}$, then the value of $f(0)$ is equal to:

0

The correct answer is Option (4) → 0

Let $f(x) = \begin{vmatrix} 0 & x - 1 & x - 2 \\ x + 1 & 0 & x - 3 \\ x + 2 & x + 3 & 0 \end{vmatrix}$

Then, $f(0) = \begin{vmatrix} 0 & -1 & -2 \\ 1 & 0 & -3 \\ 2 & 3 & 0 \end{vmatrix}$

= $0 \cdot (0 \cdot 0 - (-3) \cdot 3) - (-1) \cdot (1 \cdot 0 - (-3) \cdot 2) + (-2) \cdot (1 \cdot 3 - 0 \cdot 2)$

= $0 + 6 - 6 = 0$

∴ $f(0) = 0$