Home
Class 12
MATHS
If A and B are square matrices of ord...

If `A` and `B` are square matrices of order `n` , then prove that `A` and `B` will commute iff `A-lambda\ I` and `B-lambda\ I` commute for every scalar `lambda`

Answer

Step by step text solution for If A and B are square matrices of order n , then prove that A and B will commute iff A-lambda\ I and B-lambda\ I commute for every scalar lambda by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

Doubtnut Promotions Banner Mobile Dark
|

Similar Questions

Explore conceptually related problems

If A and B are square matrices of order n , then prove that Aa n dB will commute iff A-lambdaIa n dB-lambdaI commute for every scalar lambdadot

If A and B are symmetric matrices,then show that AB is symmetric iff AB=BA i.e.A and B commute.

Knowledge Check

  • If A and B are commuting square matrices of the same order, then which of the following is/are correct ?

    A
    A and `B^(n)` commute, `ninN`
    B
    `A^(n)` and B commute, `ninN`
    C
    `A-lamda` and `B+mu` commute, `lamda,muinR`
    D
    `A+lamda` and `B-mu` commute,`lamda,muinR`

  • If A and B matrices commute then

    A
    `A^(-1) and B ` also commute
    B
    ` B^(-1) ` and A also commute
    C
    `A^(-1) and B^(-1) ` also commute
    D
    all the above

  • If A and B are square matrices such that A^(2)= A B^(2) =B and A,B commute, then

    A
    `(AB)^(2)=I`
    B
    `(AB)^(2) = AB `
    C
    `(AB)^(2) =O`
    D
    None of these

    • Similar Questions

    Explore conceptually related problems

    If A and B are symmetric matrices of the same order,then show that AB is symmetric if and only if A and B commute,that is AB=BA

    If A and B are two square matrices such that they commute,then which of the following is true?

    " If "A" is a square matrix of order "n" ,then "|adj[lambda A)|" is equal to "

    If square matrices A and B are such that A^(2)=A,B^(2)=B and A,B commut4e for multiplication, then

    If A and B are two non singular matrices and both are symmetric and commute each other, then

    Home
    Profile