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Determinants and operations on matrices

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Definition of determinant of a matrix as a product of the diagonal entries in a non-scaled echelon form.
The determinant of a matrix can be expressed as a product of the diagonal entries in a non-scaled echelon form.
Definition of the determinant in terms of the effect of elementary row operations
The permutation expansion for determinants
A matrix and its transpose have the same determinant.
Determinants multiply: det(AB) = det(A)det(B)
The determinant of the inverse of A is the reciprocal of the determinant of A.
The determinant of a block diagonal matrix is the product of the determinants of the blocks.

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Determinants multiply: det(AB) = det(A)det(B)

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The determinant of the inverse of A is the reciprocal of the determinant of A.Close match
Determinants and operations on matricesClose match
A matrix and its transpose have the same determinant.Close match
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The determinant of a block diagonal matrix is the product of the determinants of the blocks.Close match
DeterminantsClose match
The determinant of a matrix can be expressed as a product of the diagonal entries in a non-scaled echelon form.Close match
The product of square matrices is nonsingular if and only if each factor is nonsingular.Close match
Definition of the determinant in terms of the effect of elementary row operationsClose match
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Example of multiplying 2x2 matricesClose match
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The determinant of a matrix can be computed as a cofactor expansion across any row.Close match
Multiplying a row by a scalar multiplies the determinant by that scalar.Close match
For n-by-n invertible matrices A and BClose match
Definition of determinant of a matrix as a product of the diagonal entries in a non-scaled echelon form.Close match
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