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Assertion (A) : The matrix [(cosalpha,si...

Assertion (A) : The matrix `[(cosalpha,sinalpha),(-sinalpha,cosalpha)]` is an orthogonal matrix.
Reason (R) : If A is an orthogonal matrix then `A A^(T)=A^(T)A=I`

A

Both A and R are true and R is the correct explanation of A

B

Both A and R are true R is not correct explanation of A

C

A is true R is false

D

A is false R is true

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The correct Answer is:
A
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AAKASH SERIES-MATRICES -ALGEBRA OF MATRICES - EXERCISE - II
  1. If A^(2)=2A-I then for n!=2,A^(n)=

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  2. If A=[(i,0,0),(0,i,0),(0,0,i)] then for ninN,A^(4n+1)=

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  3. If A=((0,0),(1,1)) then the value of A+A^(2)+A^(3)+ . . . .A^(n)=

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  4. If A=((2,-2,-4),(-1,3,4),(1,-2,k)) is an idempotent matrix then k =

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  5. IF A=[{:(2,4),(-1,k):}] and A^2=0 then find the value of k

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  6. A=[(1+i,2-3i,4),(7+2i,-i,3-2i)] then the conjugate of A is

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  7. If A is a skew-symmetric matrix and n is odd positive integer, then A^...

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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 [[x,4,-1]][(2,1,0),(1,0,2),(0,2,4)][(x),(4),(-1)]=0 then x=

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  10. If A=[a(ij)] is a skew symmetric matrix of order 'n' then suma(ii)=

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  11. The number of 2xx2 matrices that can be formed by using 1,2,3,4 withou...

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  12. If a matrix has 13 elements, then the possible dimensions (orders) of ...

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  13. Statement - I, The matrix [(1,-3,-4),(-1,3,4),(1,-3,-4)] is a nilpote...

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  14. Statement - I If A=[(x,1),(1,0)] is an Involutory matrix then x=0 St...

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  15. Arrange the following matrices in ascending order of value of their tr...

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  16. If A is any square matrix. Observe the following lists and matching fr...

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  17. Assertio (A) : If [(x,1),(1,0)] is an idempotent matrix then x=0 Rea...

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  18. Assertion (A) : If A=[(x,3,-10),(-3,y,9),(10,-9,z)] is a skew symmetr...

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  19. Assertion (A) : The matrix [(cosalpha,sinalpha),(-sinalpha,cosalpha)] ...

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  20. Suppose A and B are two square matrices of same order. If A, B are sym...

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