Final answer:
An invertible matrix can be expressed as a product of elementary matrices obtained by performing elementary row operations on the identity matrix.
Step-by-step explanation:
An invertible matrix can be expressed as a product of elementary matrices. An elementary matrix is obtained by performing a single elementary row operation on the identity matrix. Let's say we have an invertible matrix A. We can find the product of elementary matrices, E1, E2, ..., En, such that E1 * E2 * ... * En * A = I, where I is the identity matrix.
We can find the elementary matrices by performing the same elementary row operations on the identity matrix that were used to obtain A. Each elementary matrix represents a specific elementary row operation.
For example, if we perform row interchange on the identity matrix to obtain A, then the corresponding elementary matrix will have 1s in the diagonal positions where the rows were interchanged. By multiplying all the elementary matrices together, we can express A as their product.