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The determinant of a orthogonal matrix i...

The determinant of a orthogonal matrix is :

A

`+- 1`

B

2

C

0

D

`+- 2`

Text Solution

Verified by Experts

The correct Answer is:
A
Let A be orthogonal matrix, therefore AA
`rArr" "|"AA"^(T)|=1 rArr |A|.|A^(T)|=1`
`rArr |A|^(2)=1`
`rArr |A|=pm1`
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NDA PREVIOUS YEARS-MATRICES & DETERMINANTS-MQS
  1. The roots of the equation |{:(" "1,t-1," "1),(t-1," "1," "1),(" "1," "...

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  2. The value of the determinant |{:(m,n,p),(p,m,n),(n,p,m):}|

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  3. The determinant of a orthogonal matrix is :

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  4. If D is determinant of order 3 and D' is the determinant obtained by r...

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  5. Consider the following statements : 1. A matrix is not a number 2....

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  6. Consider the following statements : 1. The product of two non-zero m...

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  7. Consider the following statements : 1. The matrix ({:(1,2,1),(a,2a,1...

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  8. The cofactor of the element 4 in the determinant |{:(1,2,3),(4,5,6),(7...

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  9. If A is a square matrix of order 3 with |A|ne 0, then which one of the...

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  10. If A =({:(i,0),(0,-i):}),B=({:(0,-1),(1,0):}),C=({:(0,i),(i,0):}) wher...

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  11. If 2A=({:(2,1),(3,2):}), then what is A^(-1) equal to ?

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  12. If ({:(2,3),(4,1):})xx({:(5,-2),(-3,1):})=({:(1,-1),(17,lambda):}), th...

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  13. |[1,bc,bc(b+c)],[1,ca,ca(c+a)],[1,ab,ab(a+b)]|=0

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  14. Consider the following statements in respect of the matrix A=[{:(0,1,2...

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  15. Consider two matrices A=[{:(1,2),(2,1),(1,1):}]and B=[{:(1,2,-4),(2,1,...

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  16. One of the roots of |{:(x+a," "b," "c),(" "a,x+b," "c),(" "a," "b,x+c)...

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  17. If A is any matrix, then the product AA is defined only when A is a ma...

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  18. If A is a skew-symmetric matrix of odd order n , then |A|=0

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  19. If any two adjacent rows or columns of a determinant are intercharged ...

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  20. If a ne b ne c are all positive, then the value of the determinant |{:...

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