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

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2019–2026

years it has appeared

11%

rated HARD

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#1NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#2NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#3NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#4NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#5NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#6NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#7NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#8CBSE Class 12 → Mathematics → Determinants → Determinant and its Properties
#9CBSE Class 12 → Mathematics → Determinants → Determinant and its Properties
#10CBSE Class 12 → Mathematics → Determinants → Determinant and its Properties
#11CBSE Class 12 → Mathematics → Determinants → Determinant and its Properties
#12CBSE Class 12 → Mathematics → Determinants → Determinant and its Properties
#13CBSE Class 12 → Mathematics → Determinants → Determinant and its Properties
#14NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse
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#15NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse
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#16NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse
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#17NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse
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#18NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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Set · 2 questions
Consider the following for the next 02 (two) items: Let A and B be (3×3) matrices with det A = 4 and det B = 3.
- #19NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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- #20NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#21NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#22NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#23CBSE Class 12 → Mathematics → Determinants → Determinant and its Properties
#24CBSE Class 12 → Mathematics → Determinants → Adjoint and Inverse of a Matrix
#25CBSE Class 12 → Mathematics → Determinants → Adjoint and Inverse of a Matrix
#26CBSE Class 12 → Mathematics → Determinants → Determinant and its Properties
#27NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#28CBSE Class 12 → Mathematics → Determinants → Determinant and its Properties
#29CBSE Class 12 → Mathematics → Determinants → Adjoint and Inverse of a Matrix
#30CBSE Class 12 → Mathematics → Determinants → Adjoint and Inverse of a Matrix
#31NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#32NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse
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#34NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse
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#35NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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