Transpose of a Matrix ,matrix's determinant and matrice's properties

The matrix obtained by interchanging the rows into columns or vice versa is known as Transpose of a matrix .
                                                                                         
 In the diagram given above we can see how the rows become columns .The 1st row becomes the first column ,the second row becomes the second column and the third row becomes the third column .

The value that can be computed from the elements of a square matrix is known as the Determinant .

To the right is the format and an example for computing the determinant for a 2*2 matrix .


To the left is the format to compute the determinant for a 3*3 matrix .
If the matrix is known as 'A', then the determinant of the matrix A is denoted det(A), det A or |A| .

An example to understand the calculation of the determinant of a 2 * 2 matrix.

Let’s find the determinant of the matrix given below:

Below is the calculation of the determinant of a 3 * 3 matrix.

Now let's look into the properties of a matrix.

Here below are the important properties of a matrix :

Property 1 : A + B  =  B + A 

Property 2 : A + (B + C)  =  (A + B) + C 

Property 3 : A(BC)  =  (AB)C   

Property 4 : A(B + C)  =  AB + AC 

Property 5 : (A + B)C  =  AC + BC