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Given below are two statements :
Statement I : If rows and columns are interchanged and columns into rows theΒ value of the determinant remains unaltered but the sign changed.
Statement II : When two rows or columns are interchanged the numerical valueΒ of the determinant changes but the sign of the determinant remains unchanged.
In the light of the above statements, choose the most appropriate answer fromΒ the options given below:
Statement I is incorrect because when rows and columns are interchanged (taking the transpose), the value of the determinant remains completely unchanged, including its sign.
Statement II is also incorrect because interchanging any two parallel rows or two parallel columns results in the numerical value remaining the same while the sign of the determinant changes (multiplied by -1), which is the opposite of what the statement claims.
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