If, we have any given matrix A then determinant of matrix A is equal to determinant of its transpose. We can prove this by taking variable

# Archives for March 2012

## What is the determinant of a matrix if all the elements in a row or column are zero?

If in a given **matrix**, we have all zero elements in a particular row or column then **determinant** of such a **matrix** is equal to zero.

## Determinant of a Matrix having one row (column) multiple of another row (column) is equal to 0

If, we have any **matrix** in which one of the row (or column) is multiple of another row (or column) then **determinant** of such a **matrix** is equal to zero. We can prove this property by taking example of such a **matrix** and finding its **determinant**. It is one of the **property** of **determinants**. Therefore, if you see any **matrix** of the form in which one row (or column) is multiple of another row (0r column) then you can directly right value of its **determinant** equal to zero.

Let **3x 3 matrix ** {One row is multiple of another row in matrix A}

Therefore, we can see that value of **determinant** of such a **matrix** is equal to zero. Similarly, we can prove that **determinant** of **matrix** is equal to zero ( In this **matrix** we have one column multiple of another column).

## Determinant of Skew-Symmetric Matrix is equal to Zero if its order is odd

It is one of the property of skew symmetric matrix. If, we have any skew-symmetric matrix with odd order then we can directly write its determinant equal to zero. We can verify this property using an example of skew-symmetric 3x3 matrix. We can find its determinant using co-factors and can verify that its determinant is equal to zero.

## Determinant of a Matrix with two Identical rows or columns is equal to 0

It is one of the property of determinants. If, we have any matrix with two identical rows or columns then its determinant is equal to zero. We can verify this property by taking an example of matrix A such that its two rows or columns are identical.

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