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If A = [(4,5),(5,6)] show that, A^(2) = ...

If A = `[(4,5),(5,6)]` show that, `A^(2) = 10A + I` where I is the unit matrix or order 2. Hence, find the inverse of A.

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The correct Answer is:
`(1)/(17)[(4,3),(-3,2)]`
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CHHAYA PUBLICATION-ADJOINT AND INVERSE OF A MATRIX AND SOLUTION OF LINEAR SIMULTANEOUS EQUATIONS BY MATRIX METHOD-VERY SHORT ANSWER TYPE QUESTIONS
  1. Find the inverse of matrices using elementary column transformations: ...

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  2. Find the inverse of matrices using elementary column transformations: ...

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  3. Find the inverse of matrices using elementary column transformations: ...

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  4. If A =[(5,-8),(-5,8)], show by elementary row transformations that A^...

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  5. If B = [(-2,2,1),(0,4,5),(-2,6,6)], show by elementary row operations ...

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  6. If A = [(1,-2,3),(1,2,1),(-1,2,-3)] show by elementary colomn operatio...

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  7. If A =[(2,2),(4,3)] show that, AA^(-1) =I(2) wher I(2) is the unit mat...

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  8. Find the matrix A when A^(-1) = (1)/(11)[(1,4),(-2,3)]

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  9. Find the matrix A when A^(-1) = [(cos theta,sin theta),(-sin theta,...

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  10. If A =((3,1),(0,2)) show that (A^(T))^(-1) = (A^(-1))^(T) where A^(T) ...

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  11. If A =[(2,5),(1,3)] and AB = [(-13,8),(-8,5)], find B.

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  12. If A = ((4,5),(2,1)) show that, 6A^(-1) + 5I = A.

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  13. If A = [(cosalpha, sinalpha),(-sinalpha,cosalpha)] prove that, AA^(') ...

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  14. If A =[(1,-tan""(theta)/(2)),(tan""(theta)/(2), 1)] and B = [(1,tan""(...

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  15. If A = [(-3,-4),(4,5)] and B = [(2,-3),(5,-8)], verify that (AB)^(-1) ...

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  16. If A = [(2,1),(3,4)] and B = [(1,-2),(-1,1)], find the value of (AB)^(...

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  17. If A = ((3,1),(-1,2)), I = ((1,0),(0,1)) and O = ((0,0),(0,0)) show th...

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  18. If A = [(4,5),(5,6)] show that, A^(2) = 10A + I where I is the unit ma...

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  19. Show that the matrix A= [(2,-3),(3,4)] satisfies the equation x^(2) - ...

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  20. Show that, the matrix A = [(1,2,2),(2,1,2),(2,2,1)] satisfies the equa...

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