Home
Class 12
MATHS
If matrix A=[[2,-2],[-2, 2]] and A^2=p A...

If matrix `A=[[2,-2],[-2, 2]]` and `A^2=p A` , then write the value of `p`

Text Solution

Verified by Experts

Given that,
`A=[[2,-2],[-2, 2]]`
`A^2=[[2,-2],[-2, 2]][[2,-2],[-2, 2]]`
`A^2=[[8,-8],[-8, 8]]`
`A^2=pA`
`[[8,--8],[-8, 8]]=p[[2,-2],[-2, 2]]`
`p=4`

Hence, the value of `p=4`
Promotional Banner

Topper's Solved these Questions

  • ADJOINTS AND INVERSE OF MATRIX

    RD SHARMA|Exercise QUESTION|1 Videos
  • ALGEBRA OF VECTORS

    RD SHARMA|Exercise Solved Examples And Exercises|331 Videos

Similar Questions

Explore conceptually related problems

If A is a square matrix and |A|=2, then write the value of |AA'|, where A' is the transpose of matrix A

If P + P! = P^2 then the value of P is:

If A is a 2 xx 2 matrix such that |A| ne 0 " and " |A| = 5, write the value of |4A|.

if 2^(p)+3^(q)=17 and 2^(p+2)-3^(q+1)=5 then find the value of p&q

If p(x)=2+x+2x^(2)-x^(3) then find the value of p(sqrt(2))

RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. If [(a-b,2a+c),(2a-b,3c+d)]=[(-1, 5),( 0, 13)] , find the value of b

    Text Solution

    |

  2. For what value of x is the matrix A=[(0,1,-2),(1,0,3),(x,3,0)] a skew-...

    Text Solution

    |

  3. If matrix A=[[2,-2],[-2, 2]] and A^2=p A , then write the value of p

    Text Solution

    |

  4. If A is a square matrix such that A^2=A , then write the value of 7A-(...

    Text Solution

    |

  5. If 2[[3, 4, 5x]]+[[1y,0, 1]]=[[7 0, 10, 5]] , find x-y .

    Text Solution

    |

  6. If [[x,1]][(1 ,0),(-2, 0)]=O , find x

    Text Solution

    |

  7. If [a+4 3b8-6]=[2a+2b+2 8a-8b] , write the value of a-2b .

    Text Solution

    |

  8. Write a 2xx2 matrix which is both symmetric and skew-symmetric.

    Text Solution

    |

  9. If [(x y,4),(z+6,x+y)]=[(8,w),(0, 6)] , write the value of (x+y+z) .

    Text Solution

    |

  10. Construct a 2xx2 matrix A=[a(i j)] whose elements a(i j) are given by ...

    Text Solution

    |

  11. If [x+y x-y]=[2 1 4 3][1-2] , then write the value of (x ,\ y) .

    Text Solution

    |

  12. Matrix A=[0 2b-2 3 1 3 3a3-1] is given to be symmetric, find the value...

    Text Solution

    |

  13. Write the number of all possible matrices of order 2xx2 with each e...

    Text Solution

    |

  14. If [2\ \ 1\ \ 3][-1 0-1-1 1 0 0 1 1][1 0-1]=A , then write the order o...

    Text Solution

    |

  15. If A=[3 5 7 9] is written as A=P+Q , where P is symmetric and Q is sk...

    Text Solution

    |

  16. If A=[(1 ,0, 0),(0, 1,0),( a,b, -1)] , then A^2 is equal to (a) a n...

    Text Solution

    |

  17. If A=[i0 0i],\ n in N , then A^(4n) equals [0i i0] (b) [0 0 0 0] (c) ...

    Text Solution

    |

  18. If A and B are two matrices such that A B=A and B A=B , then B^...

    Text Solution

    |

  19. If A B=A and B A=B , where A and B are square matrices, then B^2=B ...

    Text Solution

    |

  20. If A and B are two matrices such that AB=B and BA=A , then A^2+B^2=

    Text Solution

    |