Determinant of a matrix remains unaltered if ______.
Options:
(A) its columns and rows are interchanged
(B) two parallel lines are identical
(C) two parallel lines intersect
(D) each element of a line is multiplied by the same factor
Official Answer Key:
A
Step-by-Step Solution & Explanation
• A fundamental determinant property: det(A) = det(Aᵀ); transposing a matrix leaves the determinant unchanged.
• Distractor logic: (B) makes the determinant zero. (C) is not a meaningful determinant operation. (D) scales the determinant by that factor, it does not leave it unaltered.
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