If w is an imaginary cube root of unity, find the value of .

Let

Using the property that if the equimultiples of corresponding elements of other rows (or columns) are added to every element of any row (or column) of a determinant, then the value of determinant remains the same

Using row transformation, R₂→R₂-ωR₁

(Since, ω is a cube root of 1, therefore ω³=1)

Using the property that if all elements of a row or column of a determinant are 0, the value of determinant is 0.

Hence ∆=0