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Let A and B be two square matrices of order 3 such that |A| = 3 and |B| = 2. Then |ATA(adj(2 A))-1(adj(4 B))(adj(AB))-1AAT| is equal to :
(3) 64
For order 3: |kM| = k3|M|, |adj M| = |M|2, | M-1| = 1|M|
|adj(2A)| = (8 3)2 = 576, |adj(4B)| = (64 2)2 = 16384, |adj(AB)| = 62 = 36
∵ |ATA| = |AAT| = 3 3 = 9
Required value = 9 1576 16384 136 9
= 81 1638420736 = 64
Answer: (3)
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