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If A = a [{:(-1, 0), (-1, 2):}]"nd B "= ...

If `A = a [{:(-1, 0), (-1, 2):}]"nd B "= [{:(3, 2), (-1, 0):}], " then find "B^(-1), A^(-1).`

A

`[{:((-1)/(2), (3)/(4)),((-1)/(2), (-5)/(4)):}]`

B

`[{:((-1)/(2), (1)/(2)),((-5)/(4), (3)/(4)):}]`

C

`[{:((1)/(2), (-1)/(2)),((-5)/(4), (3)/(4)):}]`

D

`[{:((1)/(2), (-3)/(4)),((-1)/(2), (-5)/(4)):}]`

Text Solution

Verified by Experts

The correct Answer is:
C
First find AB, after that find `(AB)^(-1)`.
We know that `(AB)^(-1) = B^(-1)A^(-1).`
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PEARSON IIT JEE FOUNDATION-MATRICES-EXERCISE CONCEPT APPLICATION (LEVEL 2)
  1. If A =((4,22),(-1,-6)), then find A +A^-1.

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  2. If A = [{:(4, p), (3, -4):}] " and " A-A^(-1) = 0, then p = .

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  3. If ({:(11, -4), (8, -3):})({:(-x, 4), (-8, y):}) = -({:(2, 3),(6, 9):}...

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  4. If [(a^x),(a^(-x))][(1,2)]=[(p,a^(- 2)),(q,log2 2)],(a >0) then a^(p...

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  5. If the matrix [{:(2^(a), 32),(36, 12^(b)):}] is singular and if k = (2...

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  6. If A =[(7,6),(-8,-7)] then find (A^12345)^-1.

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  7. The inverse of a diagonal matrix, whose principal diagonal elements ar...

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  8. If [(4^b,288),(72,18^a)] is a singular matrix and 2b = a +1/c then c ...

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  9. If A is a non-singular square matrix such that A^2-7A+5I=0, then A^-1

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  10. If A = a [{:(-1, 0), (-1, 2):}]"nd B "= [{:(3, 2), (-1, 0):}], " then ...

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  11. If P=[(secalpha,tanalpha),(-cotalpha,cosalpha)] and Q=[(-cosalpha,tan...

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  12. If A is a skew-symmetric matrix such that AB = aI, then find (A^-1)^T

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  13. If A = [{:(8, -7), (9, -8):}], " then " (A^(2007))^(-1) =.

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  14. If the matrix ({:(10, -9), (5x + 7, 5):}) is non-singular, then the ra...

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  15. If AB = BA, then prove that ABAB = A^(2)B^(2). The following are the s...

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  16. The following are the steps in finding the matrix B, if B + ({:(2, 3),...

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  17. (AB)^(-1) =.

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  18. If |{:(2, -4), (9, d-3):}|=4, then d = .

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  19. If A = ({:(2, 3), (6, 9):}), then find |A|.

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