## What are Matrices?

We can say that matrices are an elementary component of mathematics which is used in real-life problems and in higher studies. Other than mathematics, Matrices are one of the most powerful and useful means in statistics. The emergence of the concept of matrices is an outcome of an attempt to get simple and compact methods of solving the system of linear equations. Here, we shall learn about matrix formulas.

### Important Matrix Formulas and How to Calculate

1. Transpose of Matrix

If A = |aij| is the matrix of order m × n, then the matrix we get by interchanging the

rows and columns of A is what we call the transpose of A. It is depicted by AT. Thus, if A = |aij| of order m × n, then AT= |aij| of order n × m. The statement given below generalizes the transpose of a matrix:

If A = [a_{ij}]_{m×n}, then A′ =[a_{ij}]_{n×m}.

2. Inverse of Matrix

The inverse of a matrix is quite a significant operation with respect to the case of a square matrix. It is applied only for a square matrix. In order to compute the inverse, one has to determine the determinant and adjoint of that given matrix. Adjoint is provided by the transpose of a cofactor of a specific matrix. The formula to calculate the inverse of a matrix is as given, A′ = adj (A) / [A] ; [A] ≠ 0

### Matrix Algebra: Addition and Subtraction

The size of a matrix (i.e. 2 x 2) is what we call the matrix order or matrix dimension. If we need to add (or subtract) two matrices, their dimensions should be exactly the same. Simply to say, we can add a 2 x 2 matrix to another 2 x 2 matrix but not a 2 x 3 matrix. Adding matrices is quite the same as just regular addition: we just need to add the same numbers in the same position (for instance, adding all numbers in row 1, column 1, and all numbers in row 2, column 2).

### Example of Matrix Addition

Matrix addition is only a series of additions. For a 2×2 matrix, we would require to:

Sum up the top left numbers together and write the sum in a new matrix, on to the top left position.

Sum up the top right numbers together and write the sum on the top right.

Sum up the bottom left numbers together and write the sum on the bottom left.

Sum up the bottom right numbers together and write the sum on to the bottom right:

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1. What is the Matrix?

Answer: Matrix is a way of arranging the numbers, symbols and expressions in different rows and columns. Matrix formulas are incorporated to solve the set of linear equations and calculus. If the two matrices are of similar size as their rows and columns, then we can multiply and subtract them also. Apart from mathematics and statistics, Matrices are also one of the most useful tools in various areas of science like genetics. Besides, matrix and matrix formulas are used in economics, cryptography, sociology, and modern psychology, etc.

2. What is a Square Matrix?

Answer: As the name suggests, a square matrix consists of an equal number of rows and columns. Formally, we would interpret the matrix of m columns and n rows as a square if m=n. Matrices that are not square are rectangular. Note that when a square matrix does not have an inverse, it’s a singular matrix.

If we multiply the matrix by its inverse, we obtain the identity matrix, which equals 1.