NTA Abhyas JEE Main2020MathematicsMatricesPractice

A square matrix A of order 3 satisfies A 2 = Ι - 2 A , where Ι is an identity matrix of order 3 . If A n = 29 A - 12 Ι , then the value of n is equal to

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Correct answer

C. 5

Step-by-step solution

A 3 = A 2 A = Ι - 2 A A = A - 2 A 2 = A - 2 Ι - 2 A = 5 A - 2 Ι A 4 = A 3 A = 5 A - 2 Ι A = 5 A 2 - 2 A = 5 Ι - 2 A - 2 A = 5 Ι - 12 A A 5 = A 4 A = 5 Ι - 12 A A = 5 A - 12 A 2 = 5 A - 12 Ι - 2 A = 29 A - 12 Ι

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