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

If `A` is unimodular, then which of the following is unimodular?
a. `-A` b. `A^(-1)` c. `a d jA` d. `omegaA ,` where `omega` is cube root of unity

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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