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Show that costheta.[{:(costheta,sintheta...

Show that `costheta.[{:(costheta,sintheta),(-sintheta,costheta):}]+sintheta.[{:(sintheta,-costheta),(costheta,sintheta):}]=I.`

A

`{:[(-1,0),(0,-1)]:}`

B

`{:[(1,0),(0,1)]:}`

C

`{:[(1,1),(1,1)]:}`

D

`-{:[(1,1),(1,1)]:}`

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The correct Answer is:
B
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AAKASH INSTITUTE-MATRICES-Assignment (Section - A) Objective Type Questions (One option is correct)
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  2. Each diagonal elemetn of a skew symmetric matrix is (A) zero (B) negat...

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  3. If A={:[(1,0),(1,1)]:},"then "A^(2008) is equal to

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  4. If A=[ x y z],B=[(a,h,g),(h,b,f),(g ,f,c)],C=[alpha beta gamma]^T th...

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  5. if for a matrix A, A^2+I=O, where I is the identity matrix, then A equ...

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  6. If A and B are two matrices such that AB=B and BA=A, then

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  7. If {:A+B=[(1,0),(1,1)]andA-2B=[(-1,1),(0,-1)]:}," then "A=

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  8. {:[(7,1,2),(9,2,1)]:}{:[(3),(4),(5)]:}+2{:[(4),(2)]:} is equal to

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  9. If f(x)=x^(2)+4x-5andA={:[(1,2),(4,-3)]:}, then f(A) is equal to

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  10. Multiplicative inverse of the matrix [[2,1],[7,4]] is (i) [[4,-1],[-7...

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  11. If the matrix A is such that ({:(1,3),(0,1):})A=({:(1,1),(0,-1):}), t...

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  12. If A is a squqre matrix such that A^(2)=l, then A^(-1) is equal to

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  13. If X+{:[(2,1),(6,1)]:}={:[(1,1),(0,1)]:} then 'X' is equal to

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  14. If A={:[(1,2,3),(-2,5,7)]:}and2A-3B={:[(4,5,-9),(1,2,3)]:} then B is e...

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  15. If {:[(x,1),(-1,-y)]:}+{:[(y,1),(3,x)]:}={:[(1,2),(2,1)]:}, then

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  16. Let A={:[(2,3,5),(1,0,2),(3,4,5)]:}andA+B-4I=0, then B is equal to

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  17. If A={:[(1,2),(-1,8),(4,9)]:}andX+A=0, then X is equal to

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  18. Show that costheta.[{:(costheta,sintheta),(-sintheta,costheta):}]+sint...

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  19. If {:[(x+y,y-z),(z-2x,y-x)]:}={:[(3,-1),(1,1)]:}, then

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  20. If A=[{:(1,-3,2),(2," "0,2):}]" and "B=[{:(2,-1,-1),(1," "0,-1):}], fi...

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