If `A` is a square matrix such that `A*(AdjA)=[{:(4,0,0),(0,4,0),(0,0,4):}]`, then

Question

If `A` is a square matrix such that `A*(AdjA)=[{:(4,0,0),(0,4,0),(0,0,4):}]`, then

If `A` is a square matrix such that `A*(AdjA)=[{:(4,0,0),(0,4,0),(0,0,4):}]`, then
A. `|A|=4`
B. `|adjA|=16`
C. `(|adj(adjA)|)/(|adjA|)=16`
D. `|adj2A|=128`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - 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`

4 views Answered 2023-02-05 15:29