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

If A and B are square matrices of the same order such that `A B = B A`, then proveby induction that `A B^n=B^n A`. Further, prove that `(A B)^n=A^n B^n`for all `n in N`.

Text Solution

Verified by Experts

The correct Answer is:
`n in N`.
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    MODERN PUBLICATION|Exercise Exercise|7 Videos

  • MATRICES

    MODERN PUBLICATION|Exercise Revision Exercise|10 Videos

  • MATRICES

    MODERN PUBLICATION|Exercise NCERT - FILE (Question from NCERT Book) (Exercise 3.4)|14 Videos

  • LINEAR PROGRAMMING

    MODERN PUBLICATION|Exercise Chapter Test|12 Videos

  • PROBABILITY

    MODERN PUBLICATION|Exercise MOCK TEST SECTION D|6 Videos

Similar Questions

Explore conceptually related problems

If A and B are square matrices of the same order such that A B" "=" "B A , then prove by induction that A B^n=B^n A . Further, prove that (A B)^n=A^n B^n for all n in N .

If A and B are two skew symmetric matrices of order n then

If A and B are square matrices each of order n such that |A|=5,|B|=3 and |3AB|=405, then the value of n is :

Let A;B;C be square matrices of the same order n. If A is a non singular matrix; then AB=AC then B=C

If A and B are square matrices of order n xx n such that A^(2)-B^(2)=(A-B)(A+B), then which of the following will always be true?

If A and B are square matrices of size n xx n such that A^(2)-B^(2)=(A-B)(A+B), then which of the following will be always true

If A and B are any two different square matrices of order n with A^(3)=B^(3) and A(AB)=B(BA) then

If A and B are square matrices of the same order and A is non-singular,then for a positive integer n,(A^(-1)BA)^(n) is equal to A^(-n)B^(n)A^(n) b.A^(n)B^(n)A^(-n) c.A^(-1)B^(n)A d.n(A^(-1)BA)