What will be value of \(\begin{vmatrix}a & b & c \\b & c & a \\c & a & b \end {vmatrix}\)?

Given, \(\begin{vmatrix}a & b & c \\b & c & a \\c & a & b \end {vmatrix}\)
Replacing R₁ = R₁ + R₂ + R₃
\(\begin{vmatrix}a + b + c & a + b + c & a + b + c \\b & c & a \\c & a & b \end {vmatrix}\)
= (a + b + c)\(\begin{vmatrix}1 & 1 & 1 \\b & c & a \\c & a & b \end {vmatrix}\)
Replacing 2^nd column by C₂ ? C₁ and 3^rd column by C₃ ? C₁
= (a + b + c)\(\begin{vmatrix}1 & 0 & 0 \\b & c-b & a-b \\c & a-c & b-c \end {vmatrix}\)
= (a + b + c)[(c ? b)(b ? c) ? (a ? b)(a ? c)]
= (a + b + c)(bc ? b² ? c² + bc + a² + ac + ab ? bc)
= -(a + b + c)(a² + b² + c² ? ab ? bc – ac)
= -(a³ + b³ + c³ ? 3abc)