**Determinant** of any **square matrix** is equal to **determinant** of its **transpose**. Lets take an example of any **square matrix** and find value of its **determinant**. Then transpose this matrix and again find value of **determinant** of **transpose** of **matrix**. We will note that **determinant** of **matrix** is equal to **determinant** of its **transpose**.

## How to prove that det(adj(A))= (det(A)) power n-1?

**Note:** This property holds for **square matrices** which are **invertible**.

This property of adjoint of matrices can be easily proved using property

where **adj(A)** is **adjoint** of **A**, **det(A)** is determinant of **A** and is **inverse** of **A**. **A** here is an **invertible** **matrix**.

## 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**.

## 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.