If A is unimidular, then which of the fo...

If A is unimidular, then which of the following is unimodular ?

A

`-A`

B

`A^(-1)`

C

adj A

D

`omegaA`, where `omega` is cube root of unity

Text Solution

Verified by Experts

The correct Answer is:

B, C

det `(-A)=(-1)^(n)` det (A)
det `(A^(-1))=1/("det (A)")=1`
det (adj A) `=|A|^(n-1)=1`
`|omega A|=omega^(n)|A|=1` only when `n=3k, k in Z`.

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