Connection between row equivalence & the inverse

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 x 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.

The link to this playlist (Linear Algebra):

My Website:

Subscribe to My Channel to check out for more videos:

[sharshabillian]

Thanks for wasting 3 minutes of my life and not providing the proof behind why these two statements are equivalent.