Formula

Determinant of a scalar multiple

|kA| = k^{\,n}\,|A|

$k$: the scalar
$n$: the order of the matrix
$|A|$: the determinant of A

Multiplying every entry of a matrix of order n by a scalar multiplies the determinant by that scalar raised to the power n, because each of the n rows contributes one factor.

questions use it

of them past-year

2019–2026

years it has appeared

11%

rated HARD

exams

Matrices & Determinants notes Open all 35 in the paper builder

Used alongside

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

Determinant of the adjoint7
Determinant of a product7
Determinant of the inverse6
Determinant of the transpose4
The adjoint identity3
Cofactor expansion2

35 questions whose solution uses this

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

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

All Matrices & Determinants formulas