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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 transpose commutes with matrix inverse.

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Matrix inverse is an involution.Close match
Matrix transpose is an involution.Close match
Matrix inverses are unique: if A and B are square matricesClose match
Matrix adjoint is an involution.Close match
Matrix conjugation is an involution.Close match
The transpose of a product of matrices is the product of the transposes in reverse order.Close match
Transpose commutes with scalar multiplication.Close match
Definition of transpose of a matrixClose match
For n-by-n invertible matrices A and BClose match
InverseClose match
The conjugate of the transpose is the transpose of the conjugate.Close match
The inverse of a matrix (if it exists) can be found by row reducing the matrix augmented by the identity matrix.Close match
The adjoint of a product of matrices is the product of the adjoints in reverse order.Close match
The inverse of a matrix can be used to solve a linear system.Close match
The matrix of an inverse is the inverse of the matrix representationClose match
The determinant of the inverse of A is the reciprocal of the determinant of A.Close match
A matrix and its transpose have the same determinant.Close match
The inverse of a scalar multiple is the reciprocal times the inverse.Close match
A matrix turns into its adjoint when moved to the other side of the standard inner product on C^n.Close match
Example of finding the inverse of a 2-by-2 matrix by using a formulaClose match

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