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 Dec. 16, 2024 by Teachoo

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

(a) A (b) I + A

(c) I − A (d) I

This question is inspired from Misc. 15 (MCQ) - Chapter 3 Class 12 - Matrices

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Transcript

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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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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