# Elementary operations in Matrices

- Posted by aspireacademy
- Categories Maths
- Date February 28, 2023
- Comments 0 comment

**Elementary operations** of a matrix are a set of basic operations that can be performed on its rows or columns to transform it into an equivalent matrix. These operations include three types of row operations and three types of column operations.

**Row Operations**:

Interchange two rows of the matrix: In this operation, two rows are swapped with each other. This operation does not change the determinant of the matrix. It changes the sign of the determinant if the two rows are interchanged an odd number of times. For example, let’s say we have the matrix:

a. We can interchange the first and second rows to obtain:

Multiply a row by a nonzero constant: In this operation, a row is multiplied by a nonzero constant. This operation changes the determinant of the matrix by the same factor. For example, let’s say we have the matrix:

b. We can multiply the first row by 2 to obtain:

Add a multiple of one row to another row: In this operation, a multiple of one row is added to another row. This operation does not change the determinant of the matrix. For example, let’s say we have the matrix:

c. We can add 2 times the first row to the second row to obtain:

**Column Operations**

Interchange two columns of the matrix: In this operation, two columns are swapped with each other. This operation does not change the determinant of the matrix. It changes the sign of the determinant if the two columns are interchanged an odd number of times. For example, let’s say we have the matrix:

- We can interchange the first and second columns to obtain:

Multiply a column by a nonzero constant: In this operation, a column is multiplied by a nonzero constant. This operation changes the determinant of the matrix by the same factor. For example, let’s say we have the matrix:

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