Question

 Using properties of determinants, prove that: 

`|[a^2 + 1, ab, ac], [ba, b^2 + 1, bc ], [ca, cb, c^2+1]| = a^2 + b^2 + c^2 + 1`

Answer 1

L.H.S.  Δ = `|[a^2 + 1, ab, ac], [ba, b^2 + 1, bc ], [ca, cb, c^2+1]| `

Operating `R_1 → (1)/(a) R_1,R_2 → (1)/(b) R_2 and R_3 → we  have`

Δ = abc `|[a+ (1)/(a), b, c], [a , b +(1)/(b), c], [a , b , c + (1)/(c)]|`