# 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 βtwo by threeβ ) , because there are two rows and three columns.
- A matrix which possesses rows titled βXβ and columns titled as βYβ 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