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

If `{:A=[(a,0,0),(0,a,0),(0,0,a)]:}`, then the value of `abs(adjA)`, is

A

`a^27`

B

`a^9`

C

`a^6`

D

`a^2`

Text Solution

Verified by Experts

The correct Answer is:
C
Since A is a diagona matrix. Therefore,
`absA=axxa=a^3`
Also,
`abs(adjA)=abs(A)^(3-1) [:' abs(adjA)=abs(A)^(n-1)]`
`rArr abs(adjA)abs(A)^2=a^6`
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OBJECTIVE RD SHARMA-MATRICES-Section I - Solved Mcqs
  1. Let A be an inbertible matrix. Which of the following is not true?

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  2. If the matrix AB s zero, then

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  3. If {:A=[(a,0,0),(0,a,0),(0,0,a)]:}, then the value of abs(adjA), is

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

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  5. If B is a non-singular matrix and A is a square matrix, then det (B^(-...

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  6. For any 2xx2 matrix, if A\ (a d j\ A)=[10 0 0 10] , then |A| is equal ...

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  7. If A, B are square matrices of order 3,A is non0singular and AB = O, t...

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  8. If {:A=[(n,0,0),(0,n,0),(0,0,n)]and B=[(a1,a2,a3),(b1,b2,b3),(c1,c2,c3...

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  9. If A=[1a0 1] , then A^n (where n in N) equals [1n a0 1] (b) [1n^2a0 1...

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  10. If A^5=O such that A^n != I for 1 <= n <= 4, then (I - A)^-1 is equal ...

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  11. If A satisfies the equation x^3-5x^2+4x+lambda=0 , then A^(-1) exists ...

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  12. The system of equations: x+y+z=5 x+2y+3z=9 x+3y+lambdaz=mu has a un...

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  13. The matrix overset-A={:[(-i,1+2i),(-1+2i,0)]:} is which of the followi...

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  14. If {:A=[(alpha,0),(1,1)]andB=[(1,0),(5,1)]:}, then the value of alpha ...

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  15. If A and B are two square matrices such that B=-A^(-1)BA, then (A+B)^(...

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  16. The element in the first row and third column of the inverse of the ma...

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  17. A square matrix can always be expressed as

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  18. If {:[(a,b^3),(2,0)]=[(1,8),(2,0)]," then " [(a,b),(2,0)](-1)^1:}=

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  19. If A is a square matrix such that A^2-A+l=0, then the inverse of A is

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  20. If A is a 3x3 matrix and B is its adjoint matrix the determinant of B ...

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