Question

By using properties of determinants, show that:

(i)

(ii)

Answer 1

(i)

Applying R₁ → R₁ − R₃ and R₂ → R₂ − R₃, we have:

Applying R₁ → R₁ + R₂, we have:

Expanding along C₁, we have:

Hence, the given result is proved.

(ii) Let.

Applying C₁ → C₁ − C₃ and C₂ → C₂ − C₃, we have:

Applying C₁ → C₁ + C₂, we have:

Expanding along C₁, we have:

Hence, the given result is proved.