(i)
cos
–sin
sin
cos
θ
θ
θ
θ
(ii)
2 –
1
– 1
1
1
x
x
x
x
x
+
+
+
3 If
A = 
1
2
4
2






, then show that | 2A | = 4 | A |
4 If
A = 
1
0
1
0
1
2
0
0
4










, then show that | 3 A | = 27 | A |
5 Evaluate the determinants
(i)
3
–1
–2
0
0
–1
3
–5
0
(ii)
3
– 4
5
1
1
–2
2
3
1
Rationalised 2023-24
 82
MATHEMATICS
(iii)
0
1
2
–1
0
–3
–2
3
0
(iv)
2
–1
–2
0
2
–1
3
–5
0
6