The matrices are said to be singular if their determinant is equal to zero. For example, if we have matrix A whose all elements in the first column are zero. Then, by one of the property of determinants, we can say that its determinant is equal to zero. Hence, A would be called as singular matrix.

# Archives for April 2012

## Value of Determinant remains unchanged if we add equal multiples of all the elements of row (column) to corresponding elements of another row (column)

If, we have a given matrix **A**. We can perform some column and row operations on this **matrix** such that value of its determinant remains unchanged. If, we multiply particular row (column) of **matrix A** with a constant k and then add all the element of that row (column) to the corresponding elements of another row (column) then the value of **determinant** remains unchanged. This is an important property regarding **matrices and determinants**.

## Determinant of Matrix becomes k times by multiplying any row or column by k

If, we have any given **matrix** A and we multiply any row or column of **matrix** with constant k then **determinant** of modified **matrix** becomes k times of **determinant** of **A**. We can show this by taking example of **3 x 3 matrix A** and calculating its **determinant**.

## Determinant of a matrix changes sign if we interchange any two rows or columns present in a matrix

**Determinant** of a **matrix** changes its sign if we interchange any two **rows** or **columns** present in a **matrix**. We can prove this property by taking an example. We take **matrix A** and we calculate its **determinant (|A|)**.

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