Question 35 - CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1) - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at March 16, 2023 by Teachoo

If A is square matrix such that A
^{
2
}
= A, then (I + A)³ – 7 A is equal to:

Question 35 If A is square matrix such that A2 = A, then (I + A)³ – 7 A is equal to: (a) A (b) I + A (c) I − A (d) I
Given that
A2 = A
Finding (I + A)3 – 7A
(I + A)3 – 7A
Using (a + b)3 = a3 + b3 + 3a2b + 3ab2
= (I)3 + (A)3 + 3(I)2 A + 3(I)A2 – 7A
= I + A3 + 3 I A + 3A2 I – 7A
= I + A3 + 3A + 3A2 – 7A
= I + A2 . A + 3A + 3A2 – 7A
= I + A . A + 3A + 3A – 7A
= I + A2 + 6A – 7A
= I + A2 – A
= I + A – A
= I
So, the correct answer is (D)

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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