Home
Class 12
MATHS
The number of 2x2 matrices X satisfying ...

The number of `2x2` matrices `X` satisfying the matrix equation `X^2=I(Ii s2x2u n i tm a t r i x)` is 1 (b) 2 (c) 3 (d) infinite

A

0

B

1

C

2

D

more then 3

Text Solution

Verified by Experts

The correct Answer is:
D
`because X^(2) = I rArr (X^(-1) X) X=X^(-1)I`
`rArr Ix = X^(-1)`
`rArr X = X^(-1)`
which is self invertible involutory matrix.
There are many such matrices which are inverse of their own.
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|15 Videos

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|16 Videos

  • MATRICES

    ARIHANT MATHS|Exercise Exercise For Session 4|9 Videos

  • MATHEMATICAL INDUCTION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|31 Videos

Similar Questions

Explore conceptually related problems

The number of solutions of the matrix equation X^2=[1 1 2 3] is a. more than2 b. 2 c. 0 d. 1

Find the matrix X satisfying the matrix equation : [(1,2),(2,3)] X [(4,7),(3,5)] = [(1,0),(0,1)]

The number of real negative terms in the binomial expansion of (1+i x)^(4n-2),n in N ,x >0 is n b. n+1 c. n-1 d. 2n

Solve the following equation : x^2-x+1+i =0 .

Solve the following equation : x^2-(2+i)x=1-7i .

The sum of values of x satisfying the equation (31+8sqrt(15))^x^(2-3)+1=(32+8sqrt(15))^x^(2-3) is 3 b. 0 c. 2 d. none of these

Number of real values of x satisfying the equation log_(x^2+6x+8)(log_(2x^2+2x+3)(x^2-2x))=0 is equal to

Solve the following equation : x^2-(3 sqrt2 +2i)x+6 sqrt2 i=0 .

Solve the following equation : x^2-(3 sqrt2 -2i)x-6 sqrt2 i=0 .

Solve the following equation : 2x^2-(3 +7i)x + (9i-3)=0 .

ARIHANT MATHS-MATRICES -Exercise (Single Option Correct Type Questions)
  1. If A and B are two square matrices such that B=-A^(-1)BA, then (A+B)^(...

    Text Solution

    |

  2. If matrix A=[a(ij)](3xx), matrix B=[b(ij)](3xx3), where a(ij)+a(ji)=0 ...

    Text Solution

    |

  3. Let A be a nxxn matrix such thatA ^(n) = alpha A, where alpha is a ...

    Text Solution

    |

  4. If A=[[(-1+isqrt(3))/(2i),(-1-isqrt(3))/(2i)],[(1+isqrt(3))/(2i),(1-is...

    Text Solution

    |

  5. The number of 2x2 matrices X satisfying the matrix equation X^2=I(Ii s...

    Text Solution

    |

  6. if A and B are squares matrices such that A^(2006)=O and A B=A+B , the...

    Text Solution

    |

  7. Prove that: 2cos frac (pi)(13)cos frac (9pi)(13)+cos frac (3pi)(13)+co...

    Text Solution

    |

  8. There are two possible values of A in the solution of the matrix equ...

    Text Solution

    |

  9. If f (theta) = [[cos^(2) theta , cos theta sin theta,-sin theta],[cos ...

    Text Solution

    |

  10. In a square matrix A of order 3 the elements a(ii) 's are the sum of...

    Text Solution

    |

  11. If Aa n dB are two non-singular matrices of the same order such that B...

    Text Solution

    |

  12. If A=[[cos theta , sin theta],[sin theta,-costheta]], B = [[1,0],[-1,1...

    Text Solution

    |

  13. If A is a square matrix of order 3 such that abs(A)=2, then abs((adj...

    Text Solution

    |

  14. If A and B are different matrices satisfying A^(3) = B^(3) and A^(2)...

    Text Solution

    |

  15. Show that A is a symmetric matrix if A= [ (1,0), (0, -1)]

    Text Solution

    |

  16. If A = [[a,b,c],[x,y,z],[p,q,r]], B= [[q , -b,y],[-p,a,-x],[r,-c,z]] a...

    Text Solution

    |

  17. Consider three matrices A=[(2,1),(4,1)], B=[(3,4),(2,3)] and C=[(3,-4)...

    Text Solution

    |

  18. If A is non-singular and (A-2I)(A-4I)=0 , then ,1/6A+4/3A^(-1) is equa...

    Text Solution

    |

  19. If A=[[0, 1,2],[1,2,3],[3,a,1]]and A^(-1)[[1//2,-1//2,1//2],[-4,3,b],[...

    Text Solution

    |

  20. Given the matrix A=[[x,3,2],[1,y,4],[2,2,z]]. If xyz=60 and 8x+4y+3z=2...

    Text Solution

    |