Class 12 NCERT Maths – Chapter 3 (Matrices) – Exercise 3.4 Solutions

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:

Two square matrices of the same order, say A and B, are inverses of each other if and only if each is the multiplicative inverse of the other, i.e.,

AB = BA = I

This relation guarantees that both left‑ and right‑multiplication by one matrix undoes the other. Conditions involving the zero matrix or lacking the identity matrix do not satisfy this definition.

Hence, the only valid condition is (D)\;AB = BA = I.

Correct answer (D).