Using properties of determinants, prove that

OR

Let find a matrix D such that

To prove:

LHS

R₁→ R₁ + R₂ + R₃

C₂→ C₂ − C₁ and C₃→ C₃ − C₁

= 3(x+y)(2y²+y²)

= 9y²(x+y) = RHS

Hence, Proved.

OR

Given: and CD − AB = 0

Let,

∴ 2a + 5c = 3 ……(i)

2b + 5d = 0 ……(ii)

3a + 8c = 43 ……(iii)

3b + 8d = 22 ……(iv)

2(iii) − 3(i) = c = 77 ⇒ a = −191

2(iv) − 3(ii) = d = 44 ⇒ b = −110