# Learn Important Points on Matrix

The topic matrix is a very significant topic in Mathematics for JEE Exams. Since there aren’t many formulas in the matrix, students have to practise questions from this topic extensively to get a strong grip on the concepts. Students are recommended to go through the previous years’ questions and solutions of the matrix. Once the students are thorough with the concept of the matrix, it will be very easy for them to crack the problems. English mathematician James Sylvester introduced the term matrix in the 19th-century. The algebraic aspect of a matrix was developed by mathematician Arthur Cayley in the 1850s. Using a matrix, we can express the properties and operations of abstract linear algebra.

A matrix is a rectangular arrangement of real or complex numbers in the form of m horizontal lines and n vertical lines. The horizontal lines are termed as rows, and vertical lines are termed as columns. In this article, we will discuss important formulas, different types of matrices, etc.

We can represent a matrix by P = [pij] mxn. Here p11, p12, ….. etc., are known as the elements of matrix P, where pij belongs to the ith row and jth column and is called the (i, j)th element of the matrix P = [pij]. In geometry, the matrix has a wide range of applications. For example, these are used for representing and specifying coordinate changes and geometric transformations. We can also solve a large number of computational problems by reducing them to a matrix computation. It also involves computation with a matrix of huge dimensions.

The important types of the matrix are given below:

• Symmetric matrix
• Skew symmetric matrix
• Idempotent matrix
• Involuntary matrix
• Orthogonal matrix

## Important Formulas

Let P and Q represent two square matrices of the order n, and In represent the unit matrix.

(1) P.(adj P) = |P| In

(2) adj (In) = In