**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**.

## We have matrix A, how to prove that transpose of (A transpose) is equal to matrix A i.e {A^T)^T = A.

We are given **matrix A** then how can we prove that . where T represents transpose of Matrix.

Two matrices are said to be equal if they have same order and their corresponding elements are equal. Similarly, to prove . we will have to prove that both the sides have same order and both the sides have equal corresponding elements.

## We are given a matrix A and scalar k, how to prove that (kA)^T = k(A^T)?

We are given a **matrix A **and scalar **k**, we want to prove that , where **T** represents **transpose** of **matrix**.

**Two matrices** are said to be equal if they have same order and their corresponding elements are equal. Similarly, if we can prove that both the sides of equation have same order and their corresponding elements are equal then it means equation is true.

## We have two matrices A and B, how to prove that (A+B)^T is equal to A^T + B^T?

How can we prove that where A and B are two matrices of same order and T represents **transpose** of **matrix**.

Two matrices are equal if they are of same order and their corresponding elements are equal. In the same way, if we can prove that both sides of the equation have same order and their corresponding elements are equal then it means that the given equation is true.