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Question

If any two adjacent rows or columns of a determinant are interchanged in position, what will be the value of the determinant?


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Solution

Determine the value of determinant based on given information

Let us consider a 3×3 determinant

A=abcdefghi

The value of determinant A=aei-fh-bdi-fg+c(dh-eg)

Let us interchange the first and second rows of this determinant

B=defabcghi

The value of this determinant B=d(bi-ch)-e(ai-cg)+f(ah-bg)=-A

Let us interchange the first and second columns of the determinant A

C=bacedfhgi

The value of this determinant C=bdi-fg-a(ei-fh)+c(eg-dh)=-A

Hence, when two adjacent rows or columns of a determinant are interchanged, the value of the determinant changes its sign.


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