Home
Class 12
MATHS
If A is a square matrix such that A^2 = ...

If A is a square matrix such that `A^2 = I`, then `A^(-1)` is equal to (i) I (ii) 0 (iii) A (iv) I+A

A

A + 1

B

Null matrix

C

A

D

Transpose of A

Text Solution

Verified by Experts

The correct Answer is:
C
Let `A^(2) = I`
`rArr A^(2)A^(-1) = IA^(-1)`
`rArr A = A^(-1)`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    NDA PREVIOUS YEARS|Exercise MCQ|59 Videos

  • PAIR OF STRAIGHT LINES

    NDA PREVIOUS YEARS|Exercise Example|12 Videos

Similar Questions

Explore conceptually related problems

If A is a square matrix such that A^(2)=A, then (I-A)^(2)+A=

If A is a square matrix such that A^(3) =I then the value of A^(-1) is equal to

If A is a square matrix such that A^(2)= I , then (A-I)^(3)+(A+I)^(3)-7A is equal to

If A is a square matrix such that A^(2)=1 then (A-I)^(3)+(A+I)^(3)-7A is equal to

If A is a square matrix such that A^(2)=A, then (I+A)^(3)-7A is equal to (a) A (b) I-A(c)I(d)3A

If a square matrix such that A^(2)=A, then (I+A)^(3)-7A is equal to A(b)I-A(c)I (d) 3A

If A is square matrix such that A^(2)=A, then (I+A)^(3)-7A is equal to (A)A(B)I-A(C)I(D)3A

If a matrix A is such that 3A^(3)+2A^(2)+5A+I=0, then A^(-1) is equal to

NDA PREVIOUS YEARS-MATRICES & DETERMINANTS-MQS
  1. If A and B are two matrices such that A B=A and B A=B , then B^2 is...

    Text Solution

    |

  2. The sum and product of matrices A and B exist. Which of the following ...

    Text Solution

    |

  3. If A is a square matrix such that A^2 = I, then A^(-1) is equal to (i...

    Text Solution

    |

  4. If any two rows/columns of a square matrix A of order n (>2) are ident...

    Text Solution

    |

  5. If |{:(8,-5,1),(5,x,1),(6,3,1):}|=2 then what is the value of x ?

    Text Solution

    |

  6. What is the order of the product [x" "y" "z][{:(a,h,g),(h,b,f),(g,f,c)...

    Text Solution

    |

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

    Text Solution

    |

  8. If each element of as third order determinant of value /\ is multiplie...

    Text Solution

    |

  9. Inverse of diagonal matrix is (A) a diagonal matrix (B) symmetric (C) ...

    Text Solution

    |

  10. If A=[{:(3,4),(5,6),(7,8):}] and B = [{:(3,5,7),(4,6,8):}]. Then which...

    Text Solution

    |

  11. If the sum of the matrices [{:(x),(x),(y):}],[{:(y),(y),(z):}]and[{:(z...

    Text Solution

    |

  12. If the matrix AB is a zero matrix, then which one of the following is ...

    Text Solution

    |

  13. If the matrix [{:(alpha,2,2),(-3,0,4),(1,-1,1):}] is not invertible, t...

    Text Solution

    |

  14. The value of the determinant |{:(x^(2),1,y^(2)+z^(2)),(y^(2),1,z^(2)+x...

    Text Solution

    |

  15. A square matrix [a(ij)] such that a(ij)=0 for i ne j and a(ij) = k whe...

    Text Solution

    |

  16. If A and B are two non-singular square matrices such that AB = A, then...

    Text Solution

    |

  17. What is the value of the minor of the element 9 in the determinant |{:...

    Text Solution

    |

  18. The roots of the equation |{:(" "1,t-1," "1),(t-1," "1," "1),(" "1," "...

    Text Solution

    |

  19. The value of the determinant |{:(m,n,p),(p,m,n),(n,p,m):}|

    Text Solution

    |

  20. The determinant of a orthogonal matrix is :

    Text Solution

    |