As shown in the figure below, what is the value of the determinant A?

Question

Options

• A24
• B18
• C-24
• D0

• A
  5% (2)
• B
  13% (5)
• C
  3% (1)
• D
  79% (31)

Explanation

Option D (0) is correct because the matrix shown has two identical rows (or columns), which is one of the fundamental properties that forces a determinant to equal zero - a matrix with linearly dependent rows or columns is singular, and singular matrices always have a determinant of zero.

Options A (24) and C (-24) are wrong because they represent plausible cofactor expansion results that students get when they mistakenly ignore the dependency relationship and mechanically compute - they often differ only in sign, trapping students who make a row-operation sign error. Option B (18) is a common arithmetic mistake from partially computing cofactor expansions without noticing that the row/column repetition cancels everything out.

Memory tip: Think of it as "if two rows are twins, the determinant is done - it's zero." More formally, any matrix whose rows (or columns) are linearly dependent has det = 0, because the transformation it represents collapses space into a lower dimension (zero volume).

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