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Determinant of the adjoint

∣adj⁡A∣=∣A∣ n−1|\operatorname{adj}A| = |A|^{\,n-1}
AA
a square matrix
nn
the order of the matrix
∣A∣|A|
the determinant of A
adj⁡A\operatorname{adj}A
the adjugate — transpose of the cofactor matrix

The determinant of the adjugate is the determinant of the matrix raised to the power one less than the order.

43
questions use it
20
of them past-year
2020–2026
years it has appeared
23%
rated HARD
3
exams
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  • #1CBSE Class 12 → Mathematics → Determinants → Adjoint and Inverse of a Matrix

  • #2NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #3NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • Set · 1 question
    **  A\ A and BB are two matrices of same order 3×33 \times 3, where A=[123234568] and B=[325238729]A = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 3 & 4 \\ 5 & 6 & 8 \end{bmatrix}\text{~and~}B = \begin{bmatrix} 3 & 2 & 5 \\ 2 & 3 & 8 \\ 7 & 2 & 9 \end{bmatrix}

    • #4NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #5CBSE Class 12 → Mathematics → Determinants → Adjoint and Inverse of a Matrix

  • #6CBSE Class 12 → Mathematics → Determinants → Adjoint and Inverse of a Matrix

  • #7CBSE Class 12 → Mathematics → Determinants → Adjoint and Inverse of a Matrix

  • #8CBSE Class 12 → Mathematics → Determinants → Adjoint and Inverse of a Matrix

  • #9NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #10NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #11NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #12NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • Set · 1 question
    **  A\ A and BB are two matrices of same order 3×33 \times 3, where A=[123234568] and B=[325238729]A = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 3 & 4 \\ 5 & 6 & 8 \end{bmatrix}\text{~and~}B = \begin{bmatrix} 3 & 2 & 5 \\ 2 & 3 & 8 \\ 7 & 2 & 9 \end{bmatrix}

    • #13NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #14NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #15NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #16NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #17NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #18NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #19NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #20NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #21NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #22NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #23NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #24NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #25NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #26MHT-CET → Maths → Determinants and Matrices → Determinants, Cofactors and the Adjoint Identities

  • #27CBSE Class 12 → Mathematics → Determinants → Adjoint and Inverse of a Matrix

  • #28CBSE Class 12 → Mathematics → Determinants → Adjoint and Inverse of a Matrix

  • #29NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation

  • #30NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #31CBSE Class 12 → Mathematics → Determinants → Adjoint and Inverse of a Matrix

  • #32NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #33NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #34NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #35NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #36NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #37NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #38NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #39NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #40NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse

  • #41MHT-CET → Maths → Determinants and Matrices → Determinants, Cofactors and the Adjoint Identities

  • #42NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums

  • #43MHT-CET → Maths → Determinants and Matrices → Determinants, Cofactors and the Adjoint Identities

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