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Definition of left inverse of a matrix
Definition of right inverse of a matrix
Definition of inverse of a matrix
Definition of invertible matrix
If a matrix has both a left and a right inverse
If a square matrix has a one-sided inverse
Formula for the inverse of a 2-by-2 matrix.
Matrix inverse is an involution.
For n-by-n invertible matrices A and B
The product of square matrices is nonsingular if and only if each factor is nonsingular.
The inverse of a scalar multiple is the reciprocal times the inverse.
Matrix transpose commutes with matrix inverse.
The inverse of a matrix (if it exists) can be found by row reducing the matrix augmented by the identity matrix.
Example of finding the inverse of a 2-by-2 matrix by row reducing the augmented matrix
Example of finding the inverse of a 2-by-2 matrix by using a formula
Example of finding the inverse of a 3-by-3 matrix by row reducing the augmented matrix
Example of finding the inverse of a 3-by-3 matrix by using Cramer's rule
The inverse of a matrix can be used to solve a linear system.
Matrix inverses are unique: if A and B are square matrices
Definition of generalized inverse of a matrix

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Matrix inverses are unique: if A and B are square matrices

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Matrix inverse is an involution.Close match
Matrix transpose commutes with matrix inverse.Close match
If a square matrix has a one-sided inverseClose match
For n-by-n invertible matrices A and BClose match
InverseClose match
The inverse of a matrix can be used to solve a linear system.Close match
Equivalence theorem for nonsingular matrices: the matrix A has a right inverse.Close match
Equivalence theorem for nonsingular matrices: the matrix A has an inverse.Close match
Equivalence theorem for nonsingular matrices: the matrix A has a left inverse.Close match
Definition of inverse of a matrixClose match
The inverse of a matrix (if it exists) can be found by row reducing the matrix augmented by the identity matrix.Close match
If a matrix has both a left and a right inverseClose match
Matrix adjoint is an involution.Close match
The product of square matrices is nonsingular if and only if each factor is nonsingular.Close match
Definition of invertible matrixClose match
Matrix cancellation requires an invertibility or rank hypothesisClose match
The determinant of the inverse of A is the reciprocal of the determinant of A.Close match
Change of coordinates matrices are invertibleClose match
The inverse of a scalar multiple is the reciprocal times the inverse.Close match
Matrix transpose is an involution.Close match

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