1.

If A is a square matrix of order `n xx n` then adj(adj A) is equal toA. `|A|^(n)A`B. `|A|^(n-1)A`C. `|A|^(n-2)A`D. `|A|^(n-3)A`

Answer» Correct Answer - D
For any square matrix B, we have
`B("adj B")=|B|I_(n)`
On taking B=adj A, we get
(adj A)[adj (adj A)]=|adj A|`I_(n)`
`Rightarrow ` adjA[adj(adj A)]=`|A|^(n-1)I_(n) (therefore |adj A|=|A|^(n-1))`
`Rightarrow` (A adj A)[adj (adj A)]=`|A|^(n-1)A`
`Rightarrow (|A|I_(n))[adj (adj A)]=|A|^(n-1)A`
`Rightarrow` adj(adj A)=`|A|^(n-2)A`


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