if A is a square matrix of order 3, such that  / adj.A / = 64  . then find / A' / .

ans is +8 or -8

It can be explained as shown

We have

A(adj.A) = (adj.A) = |A| * I

 | A(adj.A) | =  |  |A| * I  |

|A|  |adj.A | =  |A| | I | ..... ( since | kA | = kn|A| )

|A|  |adj.A |  =  |A|n * 1

| adj.A |  =  |A|n /  |A|

This gives

| adj.A | = |A|n-1

where n is the order of the matrix.

 

So in this question

| adj.A | = |A|n-1

64 = | A | 2

|A| = +8 or -8

  • 23

 +8 or -8

  • -8

but are you asking |A| or |A|-1 ??

anyways |A|-1 = ( adj.A ) / |A|

  = 64 / ( + or - ) 8

 = +8 or - 8

  • 19

the samething again... now i am confused !

  • -6

hi tripti, i was askin abt modulus of transpose of A. tnksss ur ans. is coming out to be crrct. its a quest. in cbse sample paper.

  • 3

ok... thanx...

  • 4

Hi Anandita!
Here is the answer to your question.
 
It is known that
 
 
It is also known that
|A'| = |A|
 
∴ |A'| = 8 or –8
 
Hope! This will help you.
Cheers!!!
 

  • 35

tnk u sir, just wanted to confirm, are we multiplying both sides by A in 2nd step ?

  • 3
What are you looking for?