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If `[[alpha, beta], [gamma, -alpha]]` is to be square root of two-rowed unit matrix, then `alpha,beta` and `gamma` should satisfy the relation. a. `1-alpha^2+betagamma=0` b. `alpha^2+betagamma=0` c. `1+alpha^2+betagamma=0` d. `1-alpha^2-betagamma=0`

A

`1+alpha^2+beta gamma=0`

B

`1-alpha^2-beta gamma=0`

C

`1-alpha^2+beta gamma=0`

D

`alpha^2-beta gamma -1=0`

Text Solution

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The correct Answer is:
D
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OBJECTIVE RD SHARMA ENGLISH-MATRICES-Exercise
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  2. Which of the following is/are incorrect? (i) adjoint of a symmetri...

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  3. If [[alpha, beta], [gamma, -alpha]] is to be square root of two-rowed ...

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  4. If for matrix A,A^(2)+l=0, where l is the identity matrix, then A equa...

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  5. If A=[a(ij)](mxxn) is a matrix of rank r then (A) r=min{m,n} (B) rlemi...

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  6. If In is the identity matrix of order n, then rank of In is

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  7. A=[a(ij)](mxxn) is a square matrix, if

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  8. The rank of a null matrix is

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  9. If A is a matrix such that there exists a square submatrix of order r ...

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  10. Which of the following is correct ?

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  11. If a square matrix A is orthogonal as well as symmetric, then

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  12. Let A be a skew-symmetric of odd order, then absA is equal to

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  13. Let A be a skew-symmetric matrix of even order, then absA

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  14. If A is an orthogonal matrix, then

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  15. Let A be a non-singular square matrix of order n. Then; |adjA| =

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  16. Let A=[a(ij)](n xxn) be a square matrix and let c(ij) be cofactor of...

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  17. If A is a non-singlular square matrix of order n, then the rank of A i...

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  18. If A is a matrix such that there exists a square submatrix of order r ...

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  19. Let A be a matrix of rank r. Then,

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  20. Let A=[a(ij)](mxxn) be a matrix such that a(ij)=1 for all I,j. Then ,

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