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If A=([a(i j)])(4xx4,) such that a(i j)=...

If `A=([a_(i j)])_(4xx4,)` such that `a_(i j)={2,w h e ni=j0,w h e ni!=j ,t h e n{("det"(a d j(a d jA)))/7}` is (where {.} represents fractional part function) `1//7` b. `2//7` c. `3//7` d. none of these

A

`1/7`

B

`2/7`

C

`3/7`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
If A Is a square matrix of order, then
`abs(adj(adjS))=abs(A)^((n-1)^(2))`
We have,
`{:A=[a_(ij)]_(4xx4)=[(2,0,0,0),(0,2,0,0),(0,0,2,0),(0,0,0,2)]=2I_4:}`
`:. absA =2^4=16`
So, `abs(adj(adjA))=16^9=2^9=2^36=(2^3)^12=(7+1)^12`
`rArr 1/7abs(adj(adjA))=1/7(1+7)^12`
`=1/7(.^12C_0+^12C_1(7)+^12C_2(7)^2+...+^12C_12(7)^12)`
`rArr 1/7abs(adj(adjA))=1/7+A` natural number
`rArr {1/7abs((adj(adjA)))}=1/7`
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