Let A & B be 3*3 matrix of real numbers , where A is symmetric & , B is skew symmetric, &(A+B)(A-B)=(A-B)(A+B).if (AB)T=(-1)k AB,where (AB)T is the transpose of the matrix AB, then the possible values of k areAns=1&3

hi ayush,

(A+B)(A-B)=(A-B)(A+B)

we will get AB = BA

use dis property to get one of d values

(AB)^T = B^TA^T

so apply dis n write B^T = -B (as dis is a skew symm)

u will get(AB)^T   _=(-1) AB     (AB= BA , using d given condition)

thus getting value of k=1