Properties of matrix inversion: inverse of the inverse, inverse of the transpose, inverse of a product; elementary matrices and corresponding row operations; a matrix is invertible if and only if it is row-equivalent to the identity matrix; row-reduction algorithm for computing matrix inverse

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##### The inverse of a matrix (if it exists) can be found by row reducing the matrix augmented by the identity matrix. math.la.t.mat.inv.augmented

##### Matrix inverse is an involution. math.la.t.mat.inv.involution

##### For n-by-n invertible matrices A and B, the product AB is invertible, and (AB)^-1=B^-1 A^-1. math.la.t.mat.inv.shoesandsocks

##### Matrix transpose commutes with matrix inverse. math.la.t.mat.inv.transpose

##### Definition of elementary matrix math.la.d.mat.elementary

##### Row operations are given by multiplication by elementary matrices. math.la.d.mat.mult.elementary

##### Elementary matrices are invertible. math.la.d.mat.elementary.inv

##### Equivalence theorem: the matrix A row-reduces to the identity matrix. math.la.t.equiv.identity