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Question: \[\left| \begin{matrix} b^{2} - ab & b - c & bc - ac \\ ab - a^{2} & a - b & b^{2} - ab \\ bc - ac &...

b^{2} - ab & b - c & bc - ac \\ ab - a^{2} & a - b & b^{2} - ab \\ bc - ac & c - a & ab - a^{2} \end{matrix} \right| =$$
A

abc(a+b+c)abc(a + b + c)

B

3a2b2c23a^{2}b^{2}c^{2}

C

0

D

None of these

Answer

0

Explanation

Solution

Δ=(b−a)(b−a).∣bb−ccaa−bbcc−aa∣\Delta = (b - a)(b - a).\left| \begin{matrix} b & b - c & c \\ a & a - b & b \\ c & c - a & a \end{matrix} \right|

= (a−b)2∣bbcaabcca∣=0(a - b)^{2}\left| \begin{matrix} b & b & c \\ a & a & b \\ c & c & a \end{matrix} \right| = 0, [by C2→C2+C3C_{2} \rightarrow C_{2} + C_{3}] .