Q. 274.8( 4 Votes )

# The determinant equals

A. abc (b–c) (c – a) (a – b)

B. (b–c) (c – a) (a – b)

C. (a + b + c) (b – c) (c – a) (a – b)

D. None of these

Answer :

We have,

Taking (b – a) common from C_{1} and C_{3}, we get

Applying C_{1}→ C_{1} – C_{3}, we get

If any two columns (or rows) of a determinant are identical (all corresponding elements are same), then the value of determinant is zero.

Here, C_{1} and C_{2} are identical.

Hence, the correct option is (d).

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