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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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CENGAGE-MATRICES-Exercise (Multiple)
  1. If A is unimidular, then which of the following is unimodular ?

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  2. Let A=a("ij") be a matrix of order 3, where a("ij")={(x,,"if "i = j","...

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  3. If A=[(1,-1),(2,1)], B=[(a,1),(b,-1)] and (A+B)^(2)=A^(2)+B^(2)+2AB, t...

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  4. If AB=A and BA=Bm then which of the following is/are true ?

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  5. If A(theta)=[(sin theta, i cos theta),(i cos theta, sin theta)], then ...

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  6. Let A and B be two nonsingular square matrices, A^(T) and B^(T) are th...

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  7. If B is an idempotent matrix, and A=I-B, then

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  8. If A1=[(0, 0, 0, 1), (0, 0, 1, 0), (0, 1, 0, 0), (1, 0, 0, 0)],A2=[(0,...

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  9. Suppose a(1), a(2), .... Are real numbers, with a(1) ne 0. If a(1), a(...

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  10. If alpha, beta, gamma are three real numbers and A=[(1,cos (alpha-beta...

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  11. If D(1) and D(2) are two 3xx3 diagonal matrices, then which of the fol...

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  12. Let A be the 2 xx 2 matrix given by A=[a("ij")] where a("ij") in {0, 1...

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  13. If S=[(0,1,1),(1,0,1),(1,1,0)] and A=[(b+c,c-a,b-a),(c-b,c+b,a-b),(b-c...

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  14. P is a non-singular matrix and A, B are two matrices such that B=P^(-1...

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  15. Let A=[(1,2,2),(2,1,2),(2,2,1)]. Then

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  16. If A=[{:(1,0,0),(1,0,1),(0,1,0):}], then

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  17. If Ais symmetric and B is skew-symmetric matrix, then which of the fol...

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  18. If A=((a(i j)))(nxxn) and f is a function, we define f(A)=((f(a(i j)))...

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  19. If a is matrix such that A^(2)+A+2I=O, then which of the following is/...

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  20. If A = [(3,-3,4),(2,-3,4),(0,-1,1)], then adj (adj A) is

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