Formula

Determinant of a power

|A^m| = |A|^{\,m}

$m$: the exponent
$|A|$: the determinant of A

The determinant of a matrix power is the determinant raised to that power.

questions use it

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2017–2026

years it has appeared

22%

rated HARD

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#1Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#2Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#3Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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For the following two (02) items: Let $A=\begin{pmatrix}\cos\theta & \sin\theta\\-\sin\theta & \cos\theta\end{pmatrix}$ .
- #4Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation
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#5Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#6Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#7Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#8Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations
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#9Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations
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#10Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#11Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#12Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse
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#13Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation
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#14Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#15Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse
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#16Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#17Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse
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#18Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse
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