Formula

Adjoint of an adjoint

\operatorname{adj}(\operatorname{adj}A) = |A|^{\,n-2}\,A

$A$: a square matrix
$n$: the order of the matrix
$|A|$: the determinant of A
$\operatorname{adj}A$: the adjugate — transpose of the cofactor matrix

Taking the adjoint twice returns the matrix itself, scaled by the determinant raised to the power two less than the order.

questions use it

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2023–2026

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29%

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#1Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse
Strategy Concept notes
Set · 1 question
** $\ A$ and $B$ are two matrices of same order $3 \times 3$ , where $A = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 3 & 4 \\ 5 & 6 & 8 \end{bmatrix}\text{~and~}B = \begin{bmatrix} 3 & 2 & 5 \\ 2 & 3 & 8 \\ 7 & 2 & 9 \end{bmatrix}$
- #2Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse
  Strategy Concept notes
#3Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse
Strategy Concept notes
#4Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse
Strategy Concept notes
#5Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse
Strategy Concept notes
#6Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse
Strategy Concept notes
Set · 1 question
** $\ A$ and $B$ are two matrices of same order $3 \times 3$ , where $A = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 3 & 4 \\ 5 & 6 & 8 \end{bmatrix}\text{~and~}B = \begin{bmatrix} 3 & 2 & 5 \\ 2 & 3 & 8 \\ 7 & 2 & 9 \end{bmatrix}$
- #7Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse
  Strategy Concept notes
#8Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse
Strategy Concept notes
#9Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse
Strategy Concept notes
#10Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse
Strategy Concept notes
#11Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse
Strategy Concept notes
#12Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse
Strategy Concept notes
#13Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse
Strategy Concept notes
#14Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse
Strategy Concept notes

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