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Let a be square matrix such that A("adj....

Let a be square matrix such that `A("adj. A")=[(4,0,0),(0,4,0),(0,0,4)]`
then find the value of
(i) `|"adj. A"|` (ii) `|"adj. (adj. A)"|` (iii) `|"adj. (3A)"|`

A

`|A|=4`

B

`|adjA|=16`

C

`(|adj(adjA)|)/(|adjA|)=16`

D

`|adj2A|=128`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
`(a,b,c)` `A(adjA)=|A|I=4I`
`:.|A|=4`
`|adjA|=|A|^(3-1)=16`
`adjKA=K^(3-1)adjA`
`|adj(adjA)|=|A|^((3-1)^(2))=|A|^(4)=256`
`:. |adjKA|=(K^(3-1))^(3)|adjA|`
`:.|adj2A|=2^(6)*16`
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