Multiple choice

If any two columns of a determinant P = $\begin{vmatrix} \ 4 & 7 & 8 \ \ 3 & 1 & 5 \ \ 9 & 6 & 2 \ \end{vmatrix}$are interchanged, which of the following statements regarding the value of the determinant is correct?

  1. The absolute value remains unchanged, but the sign will change.

  2. Both the absolute value and the sign will change.

  3. The absolute value will change, but the sign will not change.

  4. Both the absolute value and the sign will remain unchanged.
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A Correct answer
Explanation

It is the fundamental property of determinant that when any two columns or rows of a determinant are interchanged, then the absolute value remains unchanged, but the sign will change.

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