The determinant $$b2$$−ab $$b-c$$ $$bc-acab$$−$$a2$$ $$a-b$$ $$b2$$−abbc−ac $$c-a$$ $$ab-a2equal$$ to

Question

The determinant $$b2$$−ab   $$b-c$$    $$bc-acab$$−$$a2$$   $$a-b$$   $$b2$$−abbc−ac   $$c-a$$    $$ab-a2equal$$ to

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we have,$$b2$$−ab   $$b-c$$    $$bc-acab$$−$$a2$$   $$a-b$$   $$b2$$−abbc−ac   $$c-a$$    $$ab-a2=b(b$$−$$a)$$   $$b-c$$    $$c(b$$−$$a)a(b$$−$$a)$$   $$a-b$$   $$b(b$$−$$a)c(b$$−$$a)$$   $$c-a$$    $$a(b$$−$$a)=(b$$−$$a)2b$$   $$b-c$$    ca   $$a-b$$   bc   $$c-a$$    a                                                         on taking (b-a) common $$C1$$ and $$C3$$ $$each=(b$$−$$a)2b$$−c   $$b-c$$    ca−b   $$a-b$$   bc−a   $$c-a$$    a                                                                 ∵$$C1$$→$$C1$$−$$C3=0since$$ two columns $$C1$$ and $$C2$$ are identical ,so the value of determinant is zero

The determinant $|\begin{array}{l} b^{2} - a b b - c b c - a c \\ a b - a^{2} a - b b^{2} - a b \\ b c - a c c - a a b - a^{2} \end{array}|$ equal to

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The determinant b2−ab b-c bc-acab−a2 a-b b2−abbc−ac c-a ab-a2equal to

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The determinant $|\begin{array}{l} b^{2} - a b b - c b c - a c \\ a b - a^{2} a - b b^{2} - a b \\ b c - a c c - a a b - a^{2} \end{array}|$ equal to