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JEE Main202118 Mar 2021Evening ShiftMathematicsMatricesActual

Let I be an identity matrix of order 2 × 2 and P = 2 - 1 5 - 3 . Then the value of n ∈ N for which P n = 5 I - 8 P is equal to ___ .

Correct answer

0

Step-by-step solution

P = 2 - 1 5 - 3 5 I - 8 P = 5 0 0 5 - 16 - 8 40 - 24 = - 11 8 - 40 29 P 2 = 2 - 1 5 - 3 2 - 1 5 - 3 = - 1 1 - 5 4 P 3 = 2 - 1 5 - 3 - 1 1 - 5 4 = 3 - 2 10 - 7 ⇒ P 6 = 3 - 2 10 - 7 3 - 2 10 - 7 = - 11 8 - 40 29 = P n ⇒ n = 6

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