If 
3 4
1
2
1
A
1 2
and B
1
2 3
0 1


−



′ = −
= 









, then verify that
(i) (A + B)′ = A′ + B′
(ii) (A – B)′ = A′ – B′
Rationalised 2023-24
MATRICES         67
4 If 
2
3
1
0
A
and B
1
2
1
2
−
−




′ =
=








, then find (A + 2B)′
5 For the matrices A and B, verify that (AB)′ = B′A′, where
(i)
[
]
1
A
4
, B
1
2
1
3




= −
= −






(ii)
[
]
0
A
1
, B
1
5
7
2
 
= 
=
 
 
 
6 If (i)
cos
sin
A
sin
cos
α
α


= 

−
α
α


, then verify that A′ A = I
(ii) If 
sin
cos
A
cos
sin
α
α


= 

−
α
α


, then verify that A′ A = I
7