CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)

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 Sept. 4, 2021 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)

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CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.