Fsc Part 1 Mathematics (Complete Solution)

Q2
Show That

if A=  
 
ι 0
1
 
, show that  A4=I2

SOLUTION:

    A   =  
 
ι 0
1
 

A4=A2.A2

=> A2=A.A

A2       =  
 
ι 0
1
 
 x
 
ι 0
1
 
 
A2       =  
 
(ι)(ι)+(0)(1) (ι)(0)+(0)(-ι)
(1)(ι)+(-ι)(1) (1)(0)+(-ι)(-ι)
 
A2       =  
 
ι2 0
0 ι2
 
A2       =  
 
-1 0
0 -1
 

then A4=A2A2

A4       =  
 
-1 0
0 -1
 
 x
 
-1 0
-1
 
 
A4       =  
 
(-1)(-1)+((0)(0) (-1)(0)+(0)(-1)
(0)(-1)+(-1)(0) (0)(0)+(-1)(-1)
 
A4       =  
 
1 0
0 1
 

=I2

Hence A4=I2

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