Home
Class 11
MATHS
Let A be a 2xx2 matrix with non-zero en...

Let A be a `2xx2` matrix with non-zero entries and let `A^(2)=I`, where I is `2xx2` identity matrix . Define `Tr(A)=` sum of diagonal elements of A and |A| = determinant of matrix A.
Statement-1 : Tr(A) = 0
Statement-2 : |A| = 1

A

Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for Statement-1

B

Statement-1 is true, Statement-2 is true, Statement-2 is not correct explanation for Statement-1

C

Statement-1 is true, Statement-2 is false

D

Statement-1 is false, Statement-2 is true

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • APPENDICES (REVISION EXERCISE)

    AAKASH SERIES|Exercise INVERSE OF A MATRIX|8 Videos

  • APPENDICES (REVISION EXERCISE)

    AAKASH SERIES|Exercise LINEAR EQUATIONS|13 Videos

  • APPENDICES (REVISION EXERCISE)

    AAKASH SERIES|Exercise ALGEBRA OF MATRICES|24 Videos

  • 3D-COORDINATE SYSTEM

    AAKASH SERIES|Exercise PRACTICE EXERCISE|40 Videos

  • CHANGE OF AXES

    AAKASH SERIES|Exercise Practice Exercise|29 Videos

Similar Questions

Explore conceptually related problems

Let A be 2xx2 matrix with non zero entries and let A^(2)=I where I is 2xx2 identity matrix. Define Tr(A)= sum of diagonal elements of A and |A|= determinant of matrix A Statement-1 Tr(A)=0 Statement -2 |A|=1

Let A be 2xx2 matrix. Statement : adj(adjA)=A Statement -2: |adjA|=|A|

If for a matrix A,A^(2)+I=O where I is the indentity matrix, then A=

If A=I is 2x2 matrix then det(I+A)=

If A=((1, 2,2),(2,1,-2),(a,2,b)) is a matrix satisfying the equation A A^(T) =9I , where I is 3xx3 identity matrix, then the ordered pair (a, b) is equal to

If A is a 4xx4 matrix and detA=-2 then det (AdjA)=

A is a symmetric matrix or skew symmetric matrix. Then A^(2) is

Show that the matrix A = {:[( 2,3),( 1,2) ]:} satisfies equation A^(2) -4A +I=0 where I is 2xx2 identity matrix and O is 2xx2 Zero matrix. Using this equation, Find A^(-1)

AAKASH SERIES-APPENDICES (REVISION EXERCISE)-DETERMINANTS
  1. If A(K)=[(K,K-1),(K-1,K)] then |A(1)|+|A(2)|+...+|A(2011)|=

    Text Solution

    |

  2. If f(x)=|(1,x,x^(2)),(x,x^(2),1),(x^(2),1,x)| then f(root(3)(2))=

    Text Solution

    |

  3. If f(x)=|(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(x-1),x(x-1)(x-2),(x+1)x(x-1)...

    Text Solution

    |

  4. |(a-b-c,2b,2c),(2a,b-c-a,2c),(2a,2b,c-a-b)|=

    Text Solution

    |

  5. |(sin theta, cos theta, sin2theta),(sin(theta+(2pi)/(3)),cos(theta+(2p...

    Text Solution

    |

  6. |(3, a+b+c, a^(2)+b^(2)+c^(2)),(a+b+c, a^(2)+b^(2)+c^(2), a^(3)+b^(3)+...

    Text Solution

    |

  7. |(1,a,a^(2)+bc),(1,b,b^(2)+ac),(1,c,c^(2)+ab)|=k(a-b),(b-c), (c-a) the...

    Text Solution

    |

  8. If A=[(0, 1,0),(0, 0,1),(-c,-b,-a)] then A^(3)+aA^(2)+bA+cI is

    Text Solution

    |

  9. If bc+ca+ab=18, and |(1,a^(2),a^(3)),(1,b^(2),b^(3)),(1,c^(2),c^(3))|=...

    Text Solution

    |

  10. If A=((1,2,1),(-1,0,3),(2,-1,1)) then characteristic equation is given...

    Text Solution

    |

  11. Let A be a 2xx2 matrix with non-zero entries and let A^(2)=I, where I...

    Text Solution

    |

  12. If alpha, beta ne 0 and f(n)=a^(n)+beta^(n) and |(3,1+f(1),1+f(2)),(1+...

    Text Solution

    |

  13. If B is a 3xx3 matrix such that B^(2)=0, then det. [(I+B)^(50)-50B]...

    Text Solution

    |

  14. If |(a^(2), b^(2), c^(2)),((a+lambda)^(2), (b+lambda)^(2), (c+lambda)^...

    Text Solution

    |

  15. If f(theta)=|(1, cos theta, 1),(-sin theta, 1,-cos theta),(-1,sin thet...

    Text Solution

    |

  16. If Delta(r )=|(r,2r-1, 3r-2),((n)/(2), n-1, a),((1)/(2)n(n-1), (n-1)^(...

    Text Solution

    |

  17. If a, b, c are sides of a scalene triangle, then the value of |(a,b,c...

    Text Solution

    |

  18. Let S={((a(11), a(12)),(a(21), a(22))):a(ij) in {0,1,2},a(11)=a(22)} ...

    Text Solution

    |

  19. If A is an 3xx3 non-singular matrix such that AA' = A'A and B=A^(-1)A'...

    Text Solution

    |

  20. The least value of the product xyz for which the determinant |(x,1,1)...

    Text Solution

    |