Evaluate

Let Δ =

Applying Row transformations

R₂→ R₂ – R₁; R₃→ R₃ – R₁

Δ =

Δ =

Now, Expanding along C₁

Δ = 1 (y × x – 0 × 0) – 0 (x × x – 0 × y) + 0 (x × 0 – y × y)

Δ = 1 (xy) – 0 + 0

Δ = xy