# Matrices: Types of Matrices and Determinant of Matrix Part 1 (For CBSE, ICSE, IAS, NET, NRA 2022)

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## What Are Matrices?

• Matrices are an important branch of mathematics, which also helps students understand other mathematical concepts due to the interrelatedness to other branches. A matrix can be defined as an array of numbers or functions arranged in a rectangular order.
• In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns.
• For example, the dimension of the matrix below is (read “two by three” ) , because there are two rows and three columns.
• A matrix which possesses rows titled “X” and columns titled as “Y” is called as a matrix of an order of . The major operations carried out with Matrices are the Addition, Subtraction, and Multiplication. Understanding the types of matrices is essential to understand, the other topics better.

## Types of Matrices

Matrices are commonly classified into:

• Column Matrix:- A matrix which consists of a singular column can be defined as a column matrix.
• For Example:
• Row Matrix:- If a matrix has only a singular row, then it is termed as a row matrix
• For example:
• Here order of A is and that of B is
• Square Matrix:- When the number of rows is equal to the number of columns, then the matrix is defined as a square matrix.
• For Example:

• Diagonal Matrix:- If the diagonal elements are zero in a square matrix, then it can be defined as a diagonal matrix.
• For Example: 0

Hence the orders of A, B and C are 1,2 and 3 respectively

• Scalar Matrix:- When the diagonal elements are equal in a diagonal matrix, then this matrix is assumed to be a Scalar matrix.
• For Example:

• Identity Matrix:- An identity matrix can be defined as a square matrix, whose elements in the diagonal are , while the other elements are zero.
• For Example:

Are identity matrices of order 1,2 and 3 respectively

• Zero Matrix:- In a matrix, when all the elements are zero, it can simply be defined as a null matrix or a zero matrix.
• For Example:

• The orders of the above matrices are and respectively
• If two square matrices called A and B exist then we can safely assume that , where B is the inverse matrix of A and A is the inverse of B. A square matrix, on the other hand, can be termed as the sum of a skew matrix and a symmetric matrix.

## Determinant of Matrix

A determinant of a matrix is the addition of the products of the elements within a square matrix. If are the elements in a matrix.

Then, the determinant is

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