When two determinants are added each of the corresponding elements gets added.

Here we can split the LHS determinant as

For the determinant u perform the following transformation R₁↔ R₃ (i.e. interchange 1^st row with 3^rd row)

When two particular rows/columns of a determinant are interchanged the value becomes negative 1 times the original value.

R₁↔ R₂ (i.e. interchange 1^st row with 2^nd row)

R1 ↔ R3 (i.e. interchange 1^st row with 3^rd row)

R1 ↔ R2 (i.e. interchange 1^st row with 2^nd row)

∴ LHS = RHS

∴