Applying Operations C₁→ C₁ + C₂ (i.e. Replacing 1^st column by addition of 1^st and 2^nd column)

C₁→ C₁ - C₃ (i.e. Replacing 1^st column by subtraction of 1^st and 3^rd column)

If any one of the rows or columns of a determinant is 0 then the value of that determinant is 0.

∴ LHS = 0 = RHS