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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.
If A and B are n-by-n matrices
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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If A and B are n-by-n matrices
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Determinants and operations on matrices