Home
Class 12
MATHS
If Aa n dB are square matrices of the sa...

If `Aa n dB` are square matrices of the same order and `A` is non-singular, then for a positive integer `n ,(A^(-1)B A)^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)B^A)^`

Promotional Banner

Similar Questions

Explore conceptually related problems

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 is a nilpotent matrix of index 2, then for any positive integer n,A(I+A)^(n) is equal to A^(-1) b.A c.A^(n) d.I_(n)

If A,B are two n xx n non-singular matrices, then

Let A,B be two matrices such that they commute.Show that for any positive integer n,AB^(n)=B^(n)A

Let A,B be two matrices such that they commute.Show that for any positive integer n,(AB)^(n)=A^(n)B^(n)

If B,C are square matrices of order n and if A=B+C,BC=CB,C^(2)=0 then which of the following is true for any positive integer N

Let A,B be two matrices such that they commute.Show that for any positive integer n,AB^(n)=B^(n)A( ii) (AB)^(n)=A^(n)B^(n)

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 .