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Grade: 12

                        

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 are Ans=1&3

11 years ago

Answers : (1)

Pratham Ashish
17 Points
							

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 = BTAT

so apply dis n write BT = -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

 

 

11 years ago
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