R₁→ cR₁ (i.e. replace 1^st row by multiplying it with c)

As we are multiplying we should also divide c so that the original given determinant is not changed

R₁→ R₁ - bR₂ (i.e. replace 1^st row by subtraction of 1^st row and b times 2^nd row)

Taking a outside the determinant from 1^st row

If any two rows or columns of a determinant are identical then the value of that determinant is 0 because we get a row or column with all elements 0 when we when we subtract those particular rows/columns here the transformation is R1 → R1 - R3

∴LHS = 0 = RHS

∴