QJEEM24Ma7d64: JEE Main 2024 Mathematics - Class 12 JEEM24Ma7d64 Solution: Let A and B be two square matrices of order 3 such that

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QJEEM24Ma7d64: JEE Main 2024 Mathematics - Class 12 JEEM24Ma7d64 Solution: Let A and B be two square matrices of order 3 such that

Let A and B be two square matrices of order 3 such that $| A | = 3$ and $| B | = 2$ . Then $| A^{T} A (adj (2 A))^{- 1} (adj (4 B)) (adj (AB))^{- 1} {AA}^{T} |$ is equal to :

Multiple Choice Options

A 32
B 81
C 64
D 108

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Accepted Answer

$\begin{aligned} | A | = 3 \\ | B | = 2 \\ | A^{T} | | A | ∣ (adj (2 A))^{- 1} ‖ adj (4 B) ‖ (adj (A B))^{- 1}) | A | | A^{T} | \\ 3 \cdot 3 \frac{1}{64 \cdot 9} (64)^{2} \cdot 4 \cdot \frac{1}{9 \cdot 4} 3 \cdot 3 \\ = 64 \end{aligned}$

QJEEM24Ma7d64: JEE Main 2024 Mathematics - Class 12 JEEM24Ma7d64 Solution: Let A and B be two square matrices of order 3 such that

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