Home
Class 12
MATHS
[" Let "A" and "B" be two square matrice...

[" Let "A" and "B" be two square matrices different from identity matrix "Psi" such that "AB=BA" and "A^(n)-B^(n)" is "],[" invertible for some positive integer 'n'.If "A^(n)-B^(n)=A^(n+1)-B^(n-1)=A^(n+2)-B^(n-2)" ,then "],[[" (A) "1-A" is singular "," (B) "1-B" is singular "," (C) "A+B=AB+1," (D) "(1-A)(1-B)" is non singular."]]

Promotional Banner

Similar Questions

Explore conceptually related problems

Let A, B be two matrices different from identify matrix such that AB=BA and A^(n)-B^(n) is invertible for some positive integer n. If A^(n)-B^(n)=A^(n+1)-B^(n+1)=A^(n+2)-B^(n+2) , then

Let A, B be two matrices different from identify matrix such that AB=BA and A^(n)-B^(n) is invertible for some positive integer n. If A^(n)-B^(n)=A^(n+1)-B^(n+1)=A^(n+1)-B^(n+2) , then

Let A, B be two matrices different from identify matrix such that AB=BA and A^(n)-B^(n) is invertible for some positive integer n. If A^(n)-B^(n)=A^(n+1)-B^(n+1)=A^(n+1)-B^(n+2) , then

Let A, B be two matrices different from identify matrix such that AB=BA and A^(n)-B^(n) is invertible for some positive integer n. If A^(n)-B^(n)=A^(n+1)-B^(n+1)=A^(n+1)-B^(n+2) , then

If AB= BA for any two square matrices , then prove by mathematical induction that (AB)^(n)=A^(n)B^(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>b and n is a positive integer,then prove that a^(n)-b^(n)>n(ab)^((n-1)/2)(a-b)

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

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