The connection between Row Equivalence & the Inverse of the matrix are materials for the math course in Introduction to Linear Algebra at the University.

❖ \(A\) is row equivalent to identity matrix if and only if \(A\) is a nonsingular (invertible, or nondegenerate) matrix.

So, \(A\) is row equivalent to the \(n \times n\) identity matrix.

❖ Two matrices \(A\) and \(B\) are Row Equivalent if it is possible to transform \(A\) into \(B\) by a sequence of Elementary Row Operations.

❖ Elementary row operations

There are three types of elementary matrices, which correspond to three types of row operations (respectively, column operations):

1. Row switching

\(A\) row within the matrix can be switched with another row.

2. Row multiplication

Each element in a row can be multiplied by a non-zero constant.

3. Row addition

\(A\) row can be replaced by the sum of that row and a multiple of another row.