**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 adj(AB)=adj(B).adj(A)?

**How to prove that adjoint(AB)= adjoint(B).adjoint(A) **if its given that **A** and **B** are two **square** and **invertible matrices**.

Using formula to calculate **inverse** of **matrix**, we can say that (1)

**adj(AB)** is **adjoint** of **(AB)** and **det(AB)** is **determinant** of **(AB)**.

(2)

## How to prove that A.adj(A)= adj(A).A=det(A).I ?

**Note:** This property holds for **square matrices**.

If, we are given **matrix A** then

How to prove that **? where ****adj(A)** is **adjoint** of **A** and **det(A)** is **determinant** of **A**.

## How to prove that adj(adjA) =A.(det(A)) power n-2 ?

## 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**.