Mathematics 9 (Complete Solutions)

Q6
Verify that

if
A =
 
1 2
0 1
 
,
B =
 
1 1
2 0
 
, then
(i) (At)t = A
(ii) (Bt)t = B

Solution:
(i) (At)t = A

R.H.S =
A =
 
1 2
0 1
 

At =
 
1 0
2 1
 

(At)t =
 
1 2
0 1
 

Hence proved L.H.S = R.H.S

(ii) (Bt)t = B

R.H.S =
B =
 
1 1
2 0
 

Bt =
 
1 2
1 0
 

(Bt)t =
 
1 1
2 0
 

Hence proved L.H.S = R.H.S

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