Matrices A and B will be inverse of each other only if
Matrices A and B will be inverse of each other only if
AB = BA
AB = BA = 0
AB = 0, BA = I
AB = BA = I
The Correct Option is D
Solution and Explanation
We know that if A is a square matrix of order m, and if there exists another square matrix B of the same order m, such that AB = BA = I, then B is said to be the inverse of A.
In this case, it is clear that A is the inverse of B.
Thus, matrices A and B will be inverses of each other only if AB = BA = I.
Top Questions on Matrices
- Which of the following can be both a symmetric and skew-symmetric matrix?
- Assertion (A): \( A = \text{diag} [3, 5, 2] \) is a scalar matrix of order \( 3 \times 3 \).
Reason (R): If a diagonal matrix has all non-zero elements equal, it is known as a scalar matrix. - If \( A \) and \( B \) are square matrices of order \( m \) such that \( A^2 - B^2 = (A - B)(A + B) \), then which of the following is always correct?
- Four friends Abhay, Bina, Chhaya, and Devesh were asked to simplify \( 4 AB + 3(AB + BA) - 4 BA \), where \( A \) and \( B \) are both matrices of order \( 2 \times 2 \). It is known that \( A \neq B \) and \( A^{-1} \neq B \). Their answers are given as:
- If \( A \) and \( B \) are square matrices of the same order, then \( (A B^T - B A^T) \) is a:
Questions Asked in CBSE CLASS XII exam
Examine Bernier's opinion on the question of land ownership in Mughal India and how were the western economists influenced by Bernier's description?
- CBSE CLASS XII - 2025
- The Mughal Empire
- Examine how did Al-Biruni compare the caste system in India with other societies and also write the chief features of his book Kitab-Ul-Hind.
- CBSE CLASS XII - 2025
- Themes in Indian History - Part I
- Analyse the ideas put forward by Bal Krishan Sharma on federalism in the Constituent Assembly.
- CBSE CLASS XII - 2025
- The Age of Industrialisation
- Analyse the causes of decline of the Vijayanagara Empire.
- CBSE CLASS XII - 2025
- Themes in Indian History - Part I
- Explain any three features of ancient Indian coinage.
- CBSE CLASS XII - 2025
- Modern Indian History and Freedom Struggle
Concepts Used:
Invertible matrices
A matrix for which matrix inversion operation exists, given that it satisfies the requisite conditions is known as an invertible matrix. Any given square matrix A of order n × n is called invertible if and only if there exists, another n × n square matrix B such that, AB = BA = In, where In is an identity matrix of order n × n.
For example,
It can be observed that the determinant of the following matrices is non-zero.
