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The determinant of a matrix can be computed as a cofactor expansion across any row.
Definition of cofactor/submatrix of a matrix
Definition of determinant of a matrix as a cofactor expansion across the first row
The determinant of a matrix can be computed as a cofactor expansion down any column.
The inverse of a matrix can be expressed in terms of its matrix of cofactors.
Cramer's rule

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The determinant of a matrix can be computed as a cofactor expansion down any column.

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The determinant of a matrix can be computed as a cofactor expansion across any row.Close match
Definition of determinant of a matrix as a cofactor expansion across the first rowClose match
CofactorsClose match
A determinant is a multilinear functionClose match
Definition of cofactor/submatrix of a matrixClose match
The inverse of a matrix can be expressed in terms of its matrix of cofactors.Close match
Determinants and operations on matricesClose match
A matrix and its transpose have the same determinant.Close match
Multiplying a row by a scalar multiplies the determinant by that scalar.Close match
Cramer's ruleClose match
Determinants multiply: det(AB) = det(A)det(B)Close match
Definition of determinant of a matrix as a product of the diagonal entries in a non-scaled echelon form.Close match
Definition of the determinant in terms of the effect of elementary row operationsClose match
The determinant of a matrix can be expressed as a product of the diagonal entries in a non-scaled echelon form.Close match
DeterminantsClose match
The determinant of the inverse of A is the reciprocal of the determinant of A.Close match
Determinants axiomaticallyClose match
The permutation expansion for determinantsClose match
The determinant of a triangular matrix is the product of the entries on the diagonal.Close match
The determinant of the matrix of a linear transformation is the factor by which the area/volume changes.Close match

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