# Square Matrix: Addition of Square Matrix and Multiplication of Square Matrix

Doorsteptutor material for CTET is prepared by world's top subject experts: fully solved questions with step-by-step explanation- practice your way to success.

Square matrix is a matrix that has an equal number of rows and columns. In mathematics, m × m matrix is called the square matrix of order m. If we multiply or add any two square matrices, the order of the resulting matrix remains the same.

For example:

In the above example, we can see, the number of rows and columns are three respectively. Since, the order of matrix is hence X is a square matrix. We can also find the determinant of a square matrix here.

Again, if we take another example, such as;

Here, the number of rows is two and the number of columns is 3. Since, rows and columns of matrix Y are not equal, hence it is not a square matrix.

Two square matrices can be added in a very simple way. Consider there is 3 by 3 matrix A and B whose values are given here:

For example:

Addition of square matrices is very important to perform. Each value in one matrix of a row is added to the other value of the same row and column of another matrix.

## Multiplication of Square Matrix

Just like the addition method, the two square matrices are multiplied in the simple way. Let us consider two 2 by 2 square matrices to be multiplied together. Hence, the resultant matrix will be:

Note: The number of rows and columns should always be the same.

### Square Matrix Determinant

The determinant of a matrix is the scalar value or a number estimated using a square matrix. The square matrix could be any number of rows and columns such as: or in the form of n × n, where the number of columns and rows are equal.

If S is the set of square matrices, R is the set of numbers (real or complex) and is defined by where and , then f (A) is called the determinant of A. The determinant of a square matrix A is denoted by or .

For a 2 by 2 matrix, the determinant is given by:

Hence, we can find the determinant using this formula.

Example: 1 If , then find .

Solution:

Here given,

On comparing the corresponding elements,

We get,

We have find