Home
Class 12
MATHS
If A is a nonsingular matrix satisfying ...

If A is a nonsingular matrix satisfying `AB-BA=A`, then prove that det. `(B+I)=` det, `(B-I)`.

Promotional Banner

Topper's Solved these Questions

  • MATRICES & DETERMINANT

    RESONANCE ENGLISH|Exercise PART-II:|28 Videos

  • INDEFINITE INTEGRATION

    RESONANCE ENGLISH|Exercise SELF PRACTIC PROBLEMS|25 Videos

  • NUMBER THEORY

    RESONANCE ENGLISH|Exercise Exercise -2 (PART - II)|4 Videos

Similar Questions

Explore conceptually related problems

If A is a skew-symmetric matrix of order 3, then prove that det A = 0 .

If A and B are non-singular symmetric matrices such that AB=BA , then prove that A^(-1) B^(-1) is symmetric matrix.

if A is a square matrix such that A^(2)=A, then det (A) is equal to

If B is a non-singular matrix and A is a square matrix, then det (B^(-1) AB) is equal to (A) det (A^(-1)) (B) det (B^(-1)) (C) det (A) (D) det (B)

If B is a non-singular matrix and A is a square matrix, then det (B^(-1) AB) is equal to (A) det (A^(-1)) (B) det (B^(-1)) (C) det (A) (D) det (B)

If A is a symmetric matrix, B is a skew-symmetric matrix, A+B is nonsingular and C=(A+B)^(-1) (A-B) , then prove that (i) C^(T) (A+B) C=A+B (ii) C^(T) (A-B)C=A-B (iii) C^(T)AC=A

If A is a nonsingular matrix such that A A^(T)=A^(T)A and B=A^(-1) A^(T) , then matrix B is

If A and B are square matrices such that AB = BA then prove that A^(3)-B^(3)=(A-B) (A^(2)+AB+B^(2)) .

If B is an idempotent matrix, and A=I-B , then

If one of the eigenvalues of a square matrix a order 3xx3 is zero, then prove that det A=0 .

RESONANCE ENGLISH-MATRICES & DETERMINANT-HLP
  1. If a,b,c are real number, and D=|{:(,a,1+2i,3-5i),(,1-2i,b,-7-3i),(,3+...

    Text Solution

    |

  2. If A=[{:(,1,a),(,0,1):}] then find lim(n-oo) (1)/(n)A^(n)

    Text Solution

    |

  3. "Let" P=[{:(,"cos"(pi)/(9),"sin"(pi)/(9)),(,-"sin"(pi)/(9),"cos"(pi)/(...

    Text Solution

    |

  4. Let A=[{:(,1,1,1),(,1,1,1),(,1,1,1):}] , B=[{:(,2,-1,-1),(,-1,2,-1),(,...

    Text Solution

    |

  5. Let A be a (4xx4) matrix such that the sum of elements in each row is ...

    Text Solution

    |

  6. Let A=[{:(,x+lambda,x,x),(,x,x+lambda,x),(,x,x,x+lambda):}]then prove ...

    Text Solution

    |

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

    Text Solution

    |

  8. Let p and q be real number such that x^(2)+px+q ne0 for every real num...

    Text Solution

    |

  9. Let A,B,C be three 3 xx 3 matrices with real enteries. If BA+BC+AC=1, ...

    Text Solution

    |

  10. If |z(1)|=|z(2)|=1, then prove that [{:(,z(1),-z(2)),(,bar(z)(2),bar(z...

    Text Solution

    |

  11. If A and B are two square matrices such that B=-A^(-1)BA, then (A+B)^(...

    Text Solution

    |

  12. about to only mathematics

    Text Solution

    |

  13. If the system of equations x=cy+bz, y=az+cx and z=bx+ay has non-trivia...

    Text Solution

    |

  14. IfD=d i ag[d1, d2, dn] , then prove that f(D)=d i ag[f(d1),f(d2), ,f(...

    Text Solution

    |

  15. Fiven the matrix A= [[-1,3,5],[1,-3,-5],[-1,3,5]] and X be the solut...

    Text Solution

    |

  16. If q is a characteristic root of an singular matrix A, then prove that...

    Text Solution

    |

  17. Show that if lambda(1), lambda(2), ...., lambda(n) are n eigenvalues o...

    Text Solution

    |

  18. If there an three square matrices A, B, C of same order satisying th...

    Text Solution

    |

  19. If A is a nonsingular matrix satisfying AB-BA=A, then prove that det. ...

    Text Solution

    |

  20. If a rank is a number associated with a matrix which is the highest or...

    Text Solution

    |