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Question

∣∣ ∣∣a1b1c1a2b2c2a3b3c3∣∣ ∣∣+∣∣ ∣∣a1a2a3b1b2b3c1c2c3∣∣ ∣∣=0


A

True

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B

False

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Solution

The correct option is B

False


Here the second matrix is the transpose of the first matrix. When we take determinant of transpose of a matrix it comes out to be the same as the original determinant. This is one of the properties of determinants. So in short both the determinants of first matrix and second matrix are equal to each other. The given expression is hence true only if the value of determinant is equal to zero. Here for a general case we cannot say that its always true. Hence the answer is false.

∣ ∣a1b1c1a2b2c2a3b3c3∣ ∣=∣ ∣a1a2a3b1b2b3c1c2c3∣ ∣


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