Fsc Part 1 Mathematics (Complete Solution)

Q9
Find the values of a and b

If A =
 
1 -1
a b
 
and A2 =
 
1 0
0 1
 
, find the values of a and b.

SOLUTION:

 A =
 
1 -1
a b
 

then

    A2  =  
 
1 0
0 1
 
A x A  =  
 
1 0
0 1
 
   
 
-1
a b
 
  
 
1 -1
a b
 
   =  
 
1 0
0 1
 
   
 
(1)(1)+(-1)(a) (1)(-1)+(-1)(b)
(a)(1)+(b)(a) (a)(-1)+(b)(b)
 
   =  
 
1 0
0 1
 
   
 
1-a -1-b
a+ab -a+b2
 
   =  
 
1 0
0 1
 

using definition of equality of matrices, we have

1-a=1

-a= 1-1

-a= 0

a=0

and

-1-b=0

-b=1

b=-1

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