Let

We know that the sign of a determinant changes if any two rows or columns are interchanged.

By interchanging R₁ and R₂, we get

By interchanging R₂ and R₃, we get

Hence,

Let us once again consider

By interchanging R₁ and R₂, we get

By interchanging C₁ and C₂, we get

Recall that the value of a determinant remains same if it its rows and columns are interchanged.

Hence,

Thus,