JEE 2023 — Mathematics PYQ

Step 1: Sabse andar wale part $|2A^{-1}|$ ko solve karte hain

Property $|kM|=k^n|M|$ ka use karke:

Kyunki $|A|=2$, isliye:

Step 2: Ab $|\text{Adj}(2A^{-1})|$ nikalte hain

Property $|\text{Adj}(M)|=|M{|}^{n-1}$ ka use karke:

Step 3: Ab $|2\cdot \text{Adj}(2A^{-1})|$ nikalte hain

Fir se $|kM|=k^n|M|$ ka use karke:

Step 4: Poore expression ka determinant nikalte hain

$|\text{Adj}(2\cdot \text{Adj}(2A^{-1}))|=|2\cdot \text{Adj}(2A^{-1}){|}^{n-1}$

Step 5: Equation bana kar $n$ ki value nikalte hain

Humein diya hai ki ye $2^{84}$ ke barabar hai:

Is cubic equation mein agar hum $n=5$ rakhte hain:

Isliye, $n=5$ sahi jawab hai.

Final Answer: $n=5$