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Let matrix A=[{:(x,y,-z),(1,2,3),(1,1,2)...

Let matrix `A=[{:(x,y,-z),(1,2,3),(1,1,2):}]` , where `x,y,z in N`. If `|adj(adj(adj(adjA)))|=4^(8)*5^(16)`, then the number of such `(x,y,z)` are

A

`28`

B

`36`

C

`45`

D

`55`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `|adj(adj(adj(adjA)))|=|A|^(16)=4^(8).5^(16)`
`implies|A|=10`
`impliesx+y+z=10`
Number of positive integral solutions is `"^(9)C_(2)=36`
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