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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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Example of finding the inverse of a 2-by-2 matrix by using a formula
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