Verified Solution • 2025–26 Session moderate

QJEEM21Ma77ec: JEE Main 2021 Mathematics - Class 12 JEEM21Ma77ec Solution: Let I be an identity matrix of order 2 2 and P = [ 2 − 1 5 − 3…

Let I be an identity matrix of order 2 ×\times 2 and P = [2−15−3]. Then the value of n ∈\in N for which Pn = 5I −- 8P is equal to ____________.

Step-by-Step Verified Solution

P=[2−15−3]

|2−λ−15−3−λ|=0

⇒\Rightarrow λ\lambda 2 + λ\lambda −- 1 = 0

⇒\Rightarrow P2 + P −- I = 0

⇒\Rightarrow P2 = I −- P

⇒\Rightarrow P4 = I + P2 −- 2P

⇒\Rightarrow P4 = 2I −- 3P

Now, P4 . P2 = (2I −- 3P)(I −- P) = 2I −- 5P + 3P2

⇒\Rightarrow P6 = 5I −- 8P

So n = 6

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