Question

Using properties of determinants prove the following:

|(1 + a, 1, 1), (1, 1 + b, 1), (1, 1, 1 + c)| = ab + bc + ca + abc

Answer 1

= abc(1 + 1/a + 1/b + 1/c) x 1 

= abc + bc + ca + ab 

LHS = abc + ab + bc + ca = RHS

Thus LHS = RHS