Let A and B be non-singular matrices of the same order such that AB=A and BA=B. Which of the following statements is/are correct? 1. A^2=A 2. AB^2=A^2B Select the correct answer using the code given below :

NDA 2022 Mathematics question

Let and be non-singular matrices of the same order such that and . Which of the following statements is/are correct? 1. 2. Select the correct answer using the code given below :

(A)1 only
(B)2 only
(C)Both 1 and 2Correct
(D)Neither 1 nor 2

Answer: (C)

Solution

Since is non-singular, . Since is non-singular, $BA = B ⇒ A

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Question ID VK-029301