Prove: `|a^2+1a b a c a bb^2+1b cc a c b c^2+1|=1+a^2+b^2+c^2`

Explanation

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


`underset(1)(R)->aunderset(1)(R)`,`underset(2)(R)->bunderset(2)(R)` and `underset(3)(R)->cunderset(3)(R)`


`implies frac{1}{abc}|[a(a^2+1),a^2b,a^2c],[ab^2,b(b^2+1),b^2c],[c^2a,c^2b,c(c^2+1)]|`


`underset(1)(C)->frac{1}{a}underset(1)(C)` and `underset(2)(C)->frac{1}{b}underset(2)(C)` and `underset(3)(C)->frac{1}{c}underset(3)(C)`



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