Home
Class 12
MATHS
Show that the matrix A = [[2,3],[1,2]sat...

Show that the matrix `A = [[2,3],[1,2]`satisfies the equation `A^2-4A+I = O`, where `I` is `2xx2` identity matrix and `O` is, `2xx2` zero matrix. Using this equation, find `A^-1`.

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    MODERN PUBLICATION|Exercise EXERCISE|326 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise EXERCISE|588 Videos

  • EXCLUSIVELY FOR JEE(ADVANCED)

    MODERN PUBLICATION|Exercise EXERCISE|38 Videos

Similar Questions

Explore conceptually related problems

Show that the matrix A = [(2,3),(1,2)] satisfies the equations A^2 - 4A +I = O . Hence find A^-1

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

If A= '[[1,2,3],[3,-2,1], [4, 2, 1]] , then find A^2-23A-40 I where I is Identify Matrix.

If A = [(3,1),(-1,2)] then the matrix A^2 - 5A + 8I is

For the matrix A = [[3,2],[1,1]] , find the numbers a and b such that A^2+aA+bI = O

Consider the matrix A = {:[(2,3),(4,5)] Show that A^2-7A-2I=O

Matrix A such that A^(2)=2A-I , where I is the identity matrix, then for n ge 2, A^(n) is equal to

If A is a square matrix such that A^2 = A , then write the value of 7A-(I+A)^3 , where I is an identity matrix.

If A is square matrix such that A^(2)=A , then write the value of 7A-(I+A)^(3) , where I is an identity matrix .

MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. Verify that (AB)^(-1) = B^(-1)A^(-1) for the matrices A and B where ...

    Text Solution

    |

  2. Verify (AB)^-1 = B^(-1)A^(-1) for the matrices A and B. Where : A = ...

    Text Solution

    |

  3. Show that the matrix A = [[2,3],[1,2]satisfies the equation A^2-4A+I =...

    Text Solution

    |

  4. If A = [[3,1],[-1,2]], show thatA^2-5A +7I = O

    Text Solution

    |

  5. For the matrix A = [[3,2],[1,1]], find the numbers a and b such that A...

    Text Solution

    |

  6. If A=[(2,-3),(-4,7)] compute A^(-1) and show that 2A^(-1) + A-9I =0

    Text Solution

    |

  7. If A= {:[(6,7),(8,9)] and B = {:[(3,2),(7,5)], find (AB)^-1

    Text Solution

    |

  8. Find the inverse of each of the following: {:[(1,-1,2),(0,2,-3),(3,-...

    Text Solution

    |

  9. Find the inverse of each of the following: {:[(1,2,3),(0,2,4),(0,0,5...

    Text Solution

    |

  10. Find the inverse of each of the following: {:[(2,1,3),(4,-1,0),(-7,2...

    Text Solution

    |

  11. Find the inverse of each of the following: {:[(1,0,0),(3,3,0),(5,2,-...

    Text Solution

    |

  12. If P = {:[(1,2,-2),(-1,3,0),(0,-2,1)], find P^-1. Verify that PP^-1= I...

    Text Solution

    |

  13. Compute (AB)^(-1) , where A=[(5,0,4),(2,3,2),(1,2,1)],B^(-1)=[(1,2,3),...

    Text Solution

    |

  14. If A={:[(1,2,2),(2,1,2),(2,2,1)], prove thst A^2-4A-5I = O and hence,...

    Text Solution

    |

  15. If A = [[2,-1,1],[-1,2,-1],[1,-1,2]], Verify that A^3-6A^2+9A-4I=O and...

    Text Solution

    |

  16. If A^-1 = [[3,-1,1],[-15,6,-5],[5,-2,2]] and B = [[1,2,-2],[-1,3,0],[0...

    Text Solution

    |

  17. Let A = [[1,-2,1],[-2,3,1],[1,1,5]] Verify that [adj A]^-1 = adj (A^-1...

    Text Solution

    |

  18. Let A = [[1,-2,1],[-2,3,1],[1,1,5]] Verify that (A^-1)^-1 = A

    Text Solution

    |

  19. Find |A|: A = {:[(1,-2,2),(2,3,5),(-2,0,1)]

    Text Solution

    |

  20. Verify A(adj A) = (adj A).A = |A|.I : [[1,-1,2],[3,0,-2],[1,0,3]]

    Text Solution

    |