math.la.t.mat.inv.involution
Statements that are equivalent to a square matrix being invertible; examples.
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
The inverse of a square matrix, and solutions to linear systems with square coefficient matrices, are intimately connected.