
Row Operations of Matrices 
There are three types of elementary matrix row operations, corresponding to the operations that apply to equations to eliminate variables: 

These operations can be done manually, but also by matrices multiplication with a given matrix and some modified identity matrix. See the three examples below. 

Adding a multiple of one row to another: 
Placing k in the second column of row 3 of the identity matrix; then multiplying the matrices. This has ktimes the values of corresponding elements of row 2 added to those of row 3 of the matrix. 

The value of the determinant in the result is identical to the value of the source matrix A. 

Multiplying a row by a nonzero scalar: 

The value of the determinant in the result is ktimes the value of the source matrix A 

Interchanging two rows: 

The value of the determinant in the result is identical to the value of the source matrix A. 

More information about determinants 
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