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If A = [(a,x),(y,a)] and if xy = 1, then...

If A = `[(a,x),(y,a)]` and if xy = 1, then det `("AA"^(T))` is equal to

A

`(a-1)^(2)`

B

`(a^(2)+1)^(2)`

C

`a^(2)-1`

D

`(a^(2)-1)^(2)`

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The correct Answer is:
A, B
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SURA PUBLICATION-MATRICES AND DETERMINANTS -EXERCISE 7.5
  1. If A= [(1,-1),(2,-1)] and B = [(a,1),(b,-1)] and(A+B)^(2)=A^(2)+B^(2),...

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  2. If A = [(1,2,2),(2,1,-2),(a,2,b)] is a matrix satisfying the equation ...

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  3. If A is a square matrix, then which of the following is not symmetric ...

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  4. If A and B are symmetric matrices of order n,where(A ne B),then:

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  5. If A = [(a,x),(y,a)] and if xy = 1, then det ("AA"^(T)) is equal to

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  6. The value of x, for which the matrix A = [(e^(x-2),e^(7+x)),(e^(2+x),e...

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  7. If the points (x,-2), (5,2), (8,8) are collinear, then x is equal to

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  8. If =|(2a,x(1),y(1)),(2b,x(2),y(2)),(2c,x(3),y(3))|=abc/2 ne 0then the ...

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  9. If the square of the matrix [(alpha,beta),(gamma,-alpha)] is the unit ...

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  10. If Delta=|(a,b,c),(x,y,z),(p,q,r)|,"then"|(ka,kb,kc),(kx,ky,kz),(kp,kq...

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  11. A root of the equation |(3-x,-6,3),(-6,3-x,3),(3,3,-6-x)|=0 is

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  12. The value of the determinant of A = [(0,a,-b),(-a,0,c),(b,-c,0)] is

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  13. If x(1), x(2), x(3) and y(1),y(2), y(3) are in arithmetic progression ...

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  14. If |.| denotes the greatest integer less than or equal to the real num...

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  15. If a ne b, b,c satisfy |(a,2b,2c),(3,b,c),(4,a,b)|=0, then abc =

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  16. If A = |(-1,2,4),(3,1,0),(-2,4,2)|and B= |(-2,4,2),(6,2,0),(-2,4,8)|,t...

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  17. If A is a skew symmetric matrix of order n and C is a column matrix of...

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  18. The matrix A satisfying the equation [(1,3),(0,1)] A= [(1,1),(0,-1)] i...

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  19. If A +I = [(3,-2),(4,1)], then (A+I) (A-I) is equal to

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  20. Let A and B be two symmetrices of same order. Then which one of the f...

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