## Quick Reference

A square matrix obtained from the identity matrix **I** by an elementary row operation. Thus there are three types of elementary matrix. Examples of each type are: The matrix (i) is obtained from **I** by interchanging the second and fifth rows, matrix (ii) by multiplying the third row by −3, and matrix (iii) by adding 4 times the fifth row to the second row. Pre-multiplication of an *m*×*n* matrix **A** by an *m*×*m* elementary matrix produces the result of the corresponding row operation on **A**.

Alternatively, an elementary matrix can be seen as one obtained from the identity matrix by an elementary column operation; and post-multiplication of an *m*×*n* matrix **A** by an *n*×*n* elementary matrix produces the result of the corresponding column operation on **A**.

*Subjects:*
Mathematics.