Home
Class 12
MATHS
Let A and B be 3xx 3 matrices of real nu...

Let `A` and `B` be `3xx 3` matrices of real numbers, where `A` is symmetric and `B` skew symmetric and `(A+B)(A-B)=(A-B)(A+B)`. If `(A B)^prime=(-1)^n A B` then,

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
B, D
`because A^(t) = A, B^(t) = -B`
Given, `(A+B) (A-B) = (A-B) (A+B) `
`rArrA^(2) - AB + BA-B^(2) = A^(2) + AB - BA-B^(2)`
`rArr AB= BA`
Also, given `(AB)^(t)=(-1)^(k)AB`
`rArr B^(t) A^(t) = (-1)^(k) AB`
`rArr -BA = (-1)^(k) AB`
`rArr (-1) = (-1)^(k) [because AB= BA]`
`therefore k = 1, 3, 5, ...`
Promotional Banner

Similar Questions

Explore conceptually related problems

If the matrix [(2,3),(5,-1)]=A +B , where A is symmetric and B is skew symmetric, then B=

If A and B are square matrices of same order and B is a skew symmetric matrix, then A'BA is Skew symmetric matrix

Express [(1,2),(3,4)] as sum of a symmetric and skew symmetric matrices.

If A and B are two square matrices of same order then (A B)^(prime)=

If A and B are symmetric matrices of the same order , then (AB-BA) is a :

If A and B are matrices of same order then (A B^prime-B A^prime) is

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

Let A and B be 3xx3 matrices such that A' = - A , B ' = B , then matrix lambdaAB+3BA is a skew - symmetric matrix for :

If A and B are symmetric matrices, then A B A is