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

FAQs on 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 A^T, is an n×m matrix where the (i,j)^th element of A becomes the (j,i)^th element of A^T.

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 I_n (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.