Prove the follow using properties [(α, α^2, β + α), (β, β^2, γ + α),(γ, γ^2, α + β)] = (β - α)(γ - α)(α - β)

Question

Prove the follow using properties

(\begin{bmatrix} \alpha&\alpha^2 & \beta + \alpha \[0.3em] \beta& \beta^2 &\gamma + \alpha \[0.3em] \gamma & \gamma^2 &\alpha + \beta \end{bmatrix})= (β - α)(γ - α)(α - β)

Answer 1

R2 = R2 - R, R3 = R3 - R1