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

If `A` is unimodular, then which of the following is unimodular? `-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`.

Doubtnut Promotions Banner Desktop Dark

Doubtnut Promotions Banner Mobile Dark

|

Topper's Solved these Questions

MATRICES
CENGAGE ENGLISH|Exercise Linked Comprehension Type|27 Videos
MATRICES
CENGAGE ENGLISH|Exercise Matrix Type|5 Videos
MATRICES
CENGAGE ENGLISH|Exercise Exercises|65 Videos
MATHMETICAL REASONING
CENGAGE ENGLISH|Exercise Archives|10 Videos
METHODS OF DIFFERENTIATION
CENGAGE ENGLISH|Exercise Single Correct Answer Type|46 Videos

Similar Questions

Explore conceptually related problems

If omega is a cube root of unity, then 1+omega = …..

If omega is a cube root of unity, then omega^(3) = ……

If omega is a cube root of unity, then 1+ omega^(2)= …..

If two fair dices are thrown and digits on dices are a and b, then find the probability for which omega^(ab) = 1 , (where omega is a cube root of unity).

Value of sum_(k = 1)^(100)(i^(k!) + omega^(k!)) , where i = sqrt(-1) and omega is complex cube root of unity , is :

Evaluate |(1,omega,omega^2),(omega,omega^2,1),(omega^2,omega, omega)| where omega is cube root of unity.

If omega is a cube root of unity, then omega + omega^(2)= …..

Prove that the lines ax+by + c = 0, bx+ cy + a = 0 and cx+ay+b=0 are concurrent if a+b+c = 0 or a+b omega + c omega^(2) + c omega = 0 where omega is a complex cube root of unity .

If omega is a cube root of unity, then find the value of the following: (1+omega-omega^2)(1-omega+omega^2)

If |z-1|lt=2a n d|omegaz-1-omega^2|=a (where omega is a cube root of unity) , then complete set of values of a

CENGAGE ENGLISH-MATRICES-Multiple Correct Answer

If A is unimodular, then which of the following is unimodular? -A b. A...
04:39
|
Let A=a0 be a matrix of order 3, where a(i j)=x ; ifi=j ,x in R, 1 if...
03:26
|
If A=[1-1 2 1],B=[a1b-1]a n d(A+B)^2=A^2+b^2+2A B ,t h e n a=-1 b. a=...
10:57
|
If AB=A and BA=B then which of the following is/are true ?
05:01
|
If A(theta)=[(sin theta, i cos theta),(i cos theta, sin theta)], then ...
07:19
|
Let A and B be two nonsingular square matrices, A^(T) and B^(T) are th...
04:03
|
If B is an idempotent matrix, and A=I-B, then
05:12
|
If A1=[(0, 0, 0, 1), (0, 0, 1, 0), (0, 1, 0, 0), (1, 0, 0, 0)],A2=[(0,...
05:26
|
Suppose a(1), a(2), .... Are real numbers, with a(1) ne 0. If a(1), a(...
05:26
|
If alpha,beta,gamma are three real numbers and A=[(1,"cos"(alpha-beta)...
03:30
|
If D(1) and D(2) are two 3xx3 diagonal matrices, then which of the fol...
04:04
|
Let A be the 2 xx 2 matrix given by A=[a("ij")] where a("ij") in {0, 1...
10:05
|
If S=[(0,1,1),(1,0,1),(1,1,0)]a n dA=[(b+c,c+a,b-c),(c-b,c+b, a-b),(b-...
05:05
|
P is a non-singular matrix and A, B are two matrices such that B=P^(-1...
06:06
|
Let A=[(1,2,2),(2,1,2),(2,2,1)] . Then A^2-4A-5I3=O b. A^(-1)=1/5(A-4...
04:58
|
If A=[{:(1,0,0),(1,0,1),(0,1,0):}], then which is true a. A^(3)-A^(2)=...
05:55
|
If Ais symmetric and B is skew-symmetric matrix, then which of the fol...
03:22
|
If A=((a(i j)))(nxxn) and f is a function, we define f(A)=((f(a(i j)))...
02:56
|
If A is a matrix such that A^2+A+2I=Odot, the which of the following i...
02:23
|
If A=[{:(3,-3,4),(2,-3,4),(0,-1,1):}] , then the trace of the matrix A...
01:49
|