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

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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.

Addition of 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