Property

Taking a common factor out of a row

\det(\ldots, kR_i, \ldots) = k\,\det(\ldots, R_i, \ldots)

A factor common to every entry of one row or column comes outside the determinant once, which is the single-row version of the scalar rule.

questions use it

of them past-year

2019–2025

years it has appeared

33%

rated HARD

exam

Used alongside

How often each of these appears in the same solution as this one.

Every one was read individually — a question is here because its solution invokes this, not because the stem mentions it.

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Showing 12 of 12 questions — easiest first, then oldest paper first.

#1Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
Strategy Concept notes
#2Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
Strategy Concept notes
#3Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
Strategy Concept notes
#4Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
Strategy Concept notes
#5Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
Strategy Concept notes
#6Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
Strategy Concept notes
#7Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
Strategy Concept notes
#8Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
Strategy Concept notes
#9Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
Strategy Concept notes
#10Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
Strategy Concept notes
#11Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
Strategy Concept notes
#12Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
Strategy Concept notes

Every identity this chapter tests, with its own question set.