Home
Class 12
MATHS
If AC=A" and "BA=B," then: "A^(2)=...

If `AC=A" and "BA=B," then: "A^(2)=`

A

A

B

B

C

I

D

O

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • MATRICES

    MARVEL PUBLICATION|Exercise TEST YOUR GRASP|26 Videos
  • MATHEMATICAL LOGIC

    MARVEL PUBLICATION|Exercise MULTIPLE CHOICE QUESTION|78 Videos
  • PAIR OF STRAIGHT LINES

    MARVEL PUBLICATION|Exercise TEST YOUR GRASP|19 Videos

Similar Questions

Explore conceptually related problems

If AB = A and BA = B, then

if AB = A and BA = B, then

If AB=A and BA=B then B^(2)=

If AB=A and BA=B, then show that A^(2)=A,B^(2)=B

If A and B are two square matrices such that AB=A and BA=B , then A^(2) equals

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

" If "AB=A,BA=B" then "A^(2)+B^(2)=[[" (A) ",A+B],[" (B) ",A-B],[" (C) ",AB],[" (D) ",O]]

If AB = A and BA = B then B'A'= A' and A'B' = B' and hence prove that A' and B' are idempotent.

MARVEL PUBLICATION-MATRICES-TEST YOUR GRASP
  1. If A is a non-singularmatrix such that A^(2)-A+I=O," then: "A^(-1)=

    Text Solution

    |

  2. If A=[(x,1),(1,0)] and A=A^(-1), then x= . . . .

    Text Solution

    |

  3. If AC=A" and "BA=B," then: "A^(2)=

    Text Solution

    |

  4. For a invertible matrix A if A(adjA)=[(10,0),(0,10)], then |A|=

    Text Solution

    |

  5. If A and B are square matrices of the same order such that A^(2)=A,B^(...

    Text Solution

    |

  6. If A={:[(2,3),(1,-1)]:}" and "A^(2)=A+B," then : "B=

    Text Solution

    |

  7. Solve system of linear equations, using matrix method, x y" "+" "2...

    Text Solution

    |

  8. If A={:[(1,2),(3,4)]:}," then: " adj(adjA)=

    Text Solution

    |

  9. If A={:[(4,2),(5,3)]:}" then :"|adj(adjA)|=

    Text Solution

    |

  10. If A={:[(2,-1,1),(1,2,1),(-1,1,3)]:}" then "|adj(adjA)|=

    Text Solution

    |

  11. If A={:[(secx,tanx),(tanx,secx)]:}" and "A(adj*A)=k{:[(1,0),(0,1)]:},"...

    Text Solution

    |

  12. If A=[[0,1] , [-1,0]]=(alphaI+betaA)^2 then alpha and beta =

    Text Solution

    |

  13. If A={:[(2,1),(3,2)]:}" and "B={:[(1,2),(-1,3)]:}," then: "B^(-1)A=

    Text Solution

    |

  14. If A={:[(2,3),(1,2)]:}" and "B={:[(3,1),(1,0)]:}," then: "B^(-1)A^(-1)...

    Text Solution

    |

  15. If square matrices A and B are such that A^(2)=A,B^(2)=B and A,B commu...

    Text Solution

    |

  16. If A=[a(ij)](3xx3) is a scalar matrix such that a(ij)=5" for all "i=j,...

    Text Solution

    |

  17. If A={:[(1,a),(0,1)]:}," then, for all "ninN," matrix "A^(n)=

    Text Solution

    |

  18. If A={:[(0,5),(4,0)]:}" and "A^(-1)=kA," then: "k=

    Text Solution

    |

  19. If f(x)=1+x+x^(2)+x^(3)" and "A={:[(0,3),(0,0)]:}," then: "f(A)=

    Text Solution

    |

  20. If A=-BAB^(-1)," then: "(A+B)^(2)=

    Text Solution

    |