Any given **square matrix A** is said to be **Invertible** if its inverse exists. In other words, we can say that **square matrix A** is said to be **Invertible** if there exists another **square matrix B** such that where **I is an identity matrix** of same order as of A and B.

## What is symmetric and skew-symmetric matrix?

**What is a Symmetric Matrix?**

A **square Matrix A** is said to be **symmetric** if **for all i and j, where is an element present at position ( row and column in ****matrix A**) and is an element present at position ( row and column in **matrix A**).

## 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.

## We are given a matrix A and scalar k then how to prove that adj(KA)=k^n-1(adjA)?

If, we are given **a** **square** **matrix A **then how to prove that ?

where, k is any scalar, **adj(A)** is **adjoint** of **matrix A** and **adj(kA)** is **adjoint** of **matrix kA.**

Using formula to find **inverse of matrices, **we can say that

, **det(kA)** represents **determinant** of **kA matrix**.