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Verify that A^(2)=I, when A=[{:(0,1,-1),...

Verify that `A^(2)=I`, when `A=[{:(0,1,-1),(4,-3,4),(3,-3,4):}]`

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To verify that \( A^2 = I \) for the matrix \[ A = \begin{pmatrix} 0 & 1 & -1 \\ 4 & -3 & 4 \\ 3 & -3 & 4 \end{pmatrix} ...
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NCERT EXEMPLAR ENGLISH-MATRICES-Solved example
  1. If A=[{:(cos q,sin q),(-sin q, cos q):}] , then variefy that A^(2)=[{:...

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  2. If A=[{:( 0,-x),(x,0):}].B=[{:(0,1),(1,0):}] and x^(2)=-1 , then show ...

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  3. Verify that A^(2)=I, when A=[{:(0,1,-1),(4,-3,4),(3,-3,4):}]

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  4. If A is a square matrix, using mathematical induction prove that (A...

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  5. Find inverse, by elementary row operations (if possible) , of both fo...

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  6. If [{:(xy,4),(z+6,x+y):}]=[{:(8,w),(0,6):}], then find the values of x...

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  7. If A=[{:(1,5),(7,12):}] and B=[{:(9,1),( 7,8):}] then find a matrix C ...

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  8. If A=[{:(3,-5),(-1,2):}] then find A^(2)-5A- 4I.

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  9. Find the values of a,b,c and d, if 3[{:(a,b),(c,d):}]=[{:(a,6),(-1,2...

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  10. Find the matrix A such that [{:(2,-1), (1,0),(-3,4):}]A=[{:(-1,-8,-10)...

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  11. If A=[{:(1,2),(4,1):}] , then find A^(2)+2A+7I.

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  12. If A=[{:(cos alpha,sin alpha),(-sin alpha, cos alpha):}] and A^(-1)=A'...

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  13. If matrix [{:(0,a,3),(2,b,-1),(c,1,0):}] is skew-symmetric matrix, the...

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  14. If P(x)=[(cosx, sinx),(-sinx, cosx)], then show that P(x).P(y)=P(x+y)=...

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  15. If A is square matrix such that A^(2)=A, then show that (I+A)^(3)=7A+I...

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  16. If A, B are square matrices of same order and B is skew-symmetric mat...

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  17. Let A ,B be two matrices such that they commute. Show that for any pos...

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  18. Find A=[(0,2y,z),(x,y,-z),(x,-y,z)] satisfies A^(T) = A^(-1)

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  19. Using elementary transformations (operations), find the inverse of the...

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  20. Express the matrix [{:(2 ,1),(3,4):}] as the sum of a symmetric and a ...

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