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`.

Promotional Banner

Topper's Solved these Questions

  • MATRICES

    NCERT GUJARATI|Exercise EXERCISE 3.4|18 Videos
  • LINEAR PROGRAMMING

    NCERT GUJARATI|Exercise MISCELLANEOUS EXERCISE|6 Videos
  • PROBABILITY

    NCERT GUJARATI|Exercise MISCELLANEOUS EXERCISE ON CHAPTER 13|18 Videos

Similar Questions

Explore conceptually related problems

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

If A and B are square matrices of same order then (A^(-1)BA)^(n) = ………… , n inN .

Let A and B are two matrices such that AB = BA, then for every n in N

If A and B are two matrices of the order 3xxmand3xxn , respectively , and m=n , then the order of matrix (5A-2B) is ……….

If A,B and C are square matrices of order n and det (A)=2, det(B)=3 and det ©=5, then find the value of 10det (A^(3)B^(2)C^(-1)).

If A, B and C are three disjoint sets such that n(A) = 9, n(B) = 7, n(c) =4 then n(AcupB cupC) = ..... .

Using mathematical induction prove that (d)/(dx) (x^(n))= n x^(n-1) for all positive integers n.

If n(A) =m and n (B)= n also total subsets of A are 16 times more than the subsets of B then m - n = ……

If a and b are distinct integers, prove that a-b is a factor of a^n - b^n , whenever n is a positive integer.

A and B are mutually disjoint sets. Then n(A cup B)="…………."