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Consider a matrix A=[a(ij)](3xx3), where...

Consider a matrix `A=[a_(ij)]_(3xx3)`, where `a_(ij)={{:(i+j","if","ij=even),(i-j","if","ij=odd):}` if `b_(ij)` is cofactor of `a_(ij)` in matrix A and `c_(ij)=sum_(r=1)^(3)a_(ir)b_(jr)`, then value of `root3(det[c_(ij)]_(3xx3))` is

A

`4`

B

`3`

C

`16`

D

`5`

Text Solution

Verified by Experts

The correct Answer is:
C
`A=[{:(0,3,-2),(3,4,5),(2,5,0):}]because|A|=16`
`thereforec_(ij)=sum_(r=1)^(3)a_(ir)b_(jr)={:{(0, if, i ne j),(|A|, if , i=j):}`
`thereforedet[c_(ij)]_(3xx3)=|A|^(2)=16^(2)`
`thereforeroot3(det[c_(ij)]_(3xx3))=16`
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