JEE Main202429 Jan 2024Evening ShiftMathematicsMatricesActual

Let A = 2 1 2 6 2 11 3 3 2 and P = 1 2 0 5 0 2 7 1 5 . The sum of the prime factors of P - 1 AP - 2 I is equal to

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Correct answer

A. 26

Step-by-step solution

Let, y = P - 1 AP - 2 I ⇒ y = P - 1 AP - 2 P - 1 P ⇒ y = P - 1 I ( A - 2 I ) P ⇒ y = P - 1 I | A - 2 I | | P | We know that, A = 1 A - 1 . ⇒ y = | A - 2 I | ⇒ y = 2 1 2 6 2 11 3 3 2 - 2 0 0 0 2 0 0 0 2 ⇒ y = 0 1 2 6 0 11 3 3 0 ⇒ y = 0 - 0 - 33 + 2 18 - 0 ⇒ y = 69 Now, prime factor of 69 is 3 and 23 . So, sum = 26

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