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If A^(-1)=[(1,-1,2),(0,3,1),(0,0,-1//3)]...

If `A^(-1)=[(1,-1,2),(0,3,1),(0,0,-1//3)]`, then

A

`|A|=-1`

B

adj `A=[(-1,1,-2),(0,-3,-1),(0,0,1//3)]`

C

`A=[(1,1//3,7),(0,1//3,1),(0,0,-3)]`

D

`A=[(1,-1//3,-7),(0,-3,0),(0,0,1)]`

Text Solution

Verified by Experts

`|A^(-1)|=-1 implies |A|=-1`
Now, use adj `A=|A|A^(-1)` and `A=(A^(-1))^(-1)`
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CENGAGE-MATRICES-Exercise (Multiple)
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  2. Let A=[(1,2,2),(2,1,2),(2,2,1)]. Then

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

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

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

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

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

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  8. If [(1,-tan theta),(tan theta,1)][(1,tan theta),(-tan theta,1)]^(-1)=[...

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  9. If A^(-1)=[(1,-1,2),(0,3,1),(0,0,-1//3)], then

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  10. If A is an invertible matrix, tehn (a d jdotA)^(-1) is equal to a d jd...

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  11. If A and B are two invertible matrices of the same order, then adj (AB...

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  12. If A, B, and C are three square matrices of the same order, then AB=AC...

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  13. If A and B are two non singular matrices and both are symmetric and co...

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  14. If A and B are square matrices of order 3 such that A^(3)=8 B^(3)=8I a...

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  15. Let A, B be two matrices different from identify matrix such that AB=B...

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  16. Let A and B be square matrices of the same order such that A^(2)=I and...

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  17. Let B is an invertible square matrix and B is the adjoint of matrix A ...

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  18. First row of a matrix A is [1,3,2]. If adj A=[(-2,4,alpha),(-1,2,1),...

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  19. Let A be a square matrix of order 3 satisfies the relation A^(3)-6A^(2...

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  20. Which of the following matericeshave eigen values as 1 and -1 ?

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