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Misc 15 - If A2 = A, then (I + A)3 - 7A  is equal to - Miscellaneous

Misc. 15 - Chapter 3 Class 12 Matrices - Part 2
Misc. 15 - Chapter 3 Class 12 Matrices - Part 3

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Misc 15 (Introduction) If A is square matrix such that A2 = A, then (I + A)3 – 7A is equal to A. A B. I − A C. I D. 3A In square matrix, Number of rows = Number of columns A is square matrix I is always a square matrix. Misc 15 If A is square matrix such that A2 = A, then (I + A)3 − 7A is equal to A. A B. I − A C. I D. 3A 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 Therefore, correct answer is C ( Putting A2 = A) ( Putting A2 = A)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.