Matrices
What is a matrix?
A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. It is often used to represent linear transformations, equations, and data.
What are the dimensions of a matrix?
The dimensions of a matrix are given by the number of rows and columns it has. For example, a matrix with m rows and n columns is said to have dimensions m×n.
What is the transpose of a matrix?
The transpose of a matrix is obtained by interchanging its rows and columns. If A is an m×n matrix, then the transpose of A, denoted by AT, is an n×m matrix where the (i,j)th element of A becomes the (j,i)th element of AT.
What is a square matrix?
A square matrix is a matrix that has an equal number of rows and columns (i.e., m = n). Square matrices are often encountered in various mathematical operations and applications.
What is a diagonal matrix?
A diagonal matrix is a square matrix where all the elements outside the main diagonal (from the top left to the bottom right) are zero. The main diagonal contains the non-zero elements.
What is the identity matrix?
The identity matrix, denoted by I or In (where n represents the size of the square matrix), is a special diagonal matrix where all the elements on the main diagonal are 1 and all other elements are 0.
NCERT Solutions Class 12 – Mathematics Part I – Chapter 3 Matrices – Exercise 3.4
Question 1. Matrices A and B will be inverse of each other only if:
(A) AB = BA
(B) AB = BA = 0
(C) AB = 0, BA = I
(D) AB = BA = I
Solution:
According to the definition of inverse of square matrix,
Option (D) is correct
i.e. AB=BA=I