8 For the matrix 
1
5
A
6
7


= 



, verify that
(i) (A + A′) is a symmetric matrix
(ii) (A – A′) is a skew symmetric matrix
9 Find 
(
)
1 A
A
2
′
+
 and 
(
)
1 A
A
2
′
−
, when 
0
A
0
0
a
b
a
c
b
c




= −




−
−


10 Express the following matrices as the sum of a symmetric and a skew symmetric
matrix:
Rationalised 2023-24
 68
MATHEMATICS
(i)
3
5
1
1



−


(ii)
6
2
2
2
3
1
2
1
3
−




−
−




−


(iii)
3
3
1
2
2
1
4
5
2
−




−
−




−
−


(iv)
1
5
1
2




−

Choose the correct answer in the Exercises 11 and 12