Elementary Matrix Operations

Elementary row (column) operations:

1. interchanging any two rows (columns)
2. multiplying any row (column) by a nonzero scalar
3. adding any scalar multiple of a row (column) to another row (column)

Elementary Matrices

• An elementary matrix is a matrix obtained after performing an elementary operation on $I_n$
• Multiplying by an elementary matrix is equivalent to applying the operation
• Elementary matrices are invertible and the inverse is of the same type