# Equivalence theorem: the matrix A row-reduces to the identity matrix.

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# Invertible Matrix Theorem

Statements that are equivalent to a square matrix being invertible; examples.

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August 21st, 2017
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# Matrix inverses

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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August 25th, 2017
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# Nonsingular Matrices - A First Course in Linear Algebra

In this section we specialize further and consider matrices with equal numbers of rows and columns, which when considered as coefficient matrices lead to systems with equal numbers of equations and variables. We will see in the second half of the course (Chapter D, Chapter E, Chapter LT, Chapter R) that these matrices are especially important.