Equality of Matrices : Matrices Operations Part-1

Equality of matrices is first part of natricx operations. In earlier posts we have seen the Basic introduction and types of matrices.  

Equality of Matrices

If we have two matrices A and B, both are 2 x 2 order square matrices. Then A and B will be equal provided their corresponding elements are same.

From this example you will observe;

From the above example; for A matrix, a₁₁=5; a₁₂=7; a₁₃=6

for B matrix b₁₁=5; b₁₂=7; b₁₃=6

so a₁₁= b₁₁ ; a₁₂= b₁₂ ;a₁₃= b₁₃

Different order of matrices 

It is simple, but what if the orders  are different of the matrices?

Are these equal matrices? Obviously No !!

Because matrix A has the (first one in left side) 3 rows by 2 columns order, while right side the matrix B is a square matrix of the 3 x 3 order. 

So there is no possibility of the comparision. This is not allowed.

Conclusion

In conclusion you can say that matrices order is important to define the two equal matrices. Only a specific types of the matrices can define the nature of the matrices. If you are using rectangulat matrices then also all the elements of the matrices should be same.

In case of three similar dimension matrices A , B and C; 

If matrix A = matrix B, and matrix B = matrix C, then matrix A = matrix C 

READ ALSO:

1. Types of Matrices for the Maths Matrix Beginner
2. Matrices an Introduction

For any help you can comment in the comment box.