Matrices.

Number Theory Level 3

Let A A be a non-singular matrix of order 3 × 3 3\times3 and matrices B B , C C and D D are related such that B = a d j ( A ) B=adj(A) , C = a d j ( a d j ( A ) ) C=adj(adj(A)) , D = ( a d j ( a d j ( a d j ( A ) ) ) D=(adj(adj(adj(A))) . If ∣ a d j ( a d j ( a d j ( a d j A B C D ) ) ) ∣ |adj(adj(adj(adjABCD)))| is ∣ A ∣ k |A|^k , then k k

Cannot say is an odd number is less than 256 256 has 21 21 divisors

Sahil Silare by Sahil Silare , 20, India

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1 solution

Ankit Kumar Jain
Mar 31, 2018

@Sahil Silare Why did you choose 'less than 256' as one of the options? What was the correct answer (exact value of k)?, maybe I have got it correct by chance.. Please help.

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K K was coming out to be 240 240 I'll give you solution afterwards I'm a bit busy right now.

Sahil Silare - 3 years, 2 months ago

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I got the same.

Ankit Kumar Jain - 3 years, 2 months ago

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After JEE main I'll give the solution

Sahil Silare - 3 years, 2 months ago

Me too!!! :P .. Why am I so excited? Lol

Md Zuhair - 2 years, 11 months ago

The answer is 240 , if you wanna be sure

prashant pareek - 2 years, 11 months ago

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Yeah correct. Got the same

Md Zuhair - 2 years, 11 months ago

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