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Question

Let A be a matrix of order 3×3 and matrices B, C, D are related such that B = adj(A), C = adj(adj A), D \(= adj (adj(adj(A)))\). If |adj(adj(adj(adj(ABCD))))| is Ak then k 


Correct Answer
A
Is less than 256
Your Answer
B
Has 21 divisors
Your Answer
C
Greater than 256
Your Answer
D
Is an odd number

Solution

The correct option is D Is less than 256
Let ABCD = E
|adj(adj(adj(adj(ABCD))))|
=|adj(adj(adj(adj(E))))|
=|E|(31)4=|E|16
=|ABCD|16=|A|16|B|16|C|16|D|16
=|A|16.(|A|31)16.(|A|(31)2)16.(|A|(31)3)16
=|A|16+32+64+128=AK
K=240; which is less than 256.

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