Observe that, |A| = 4(– 2) = 22|B| or |A| = 2n|B|, where n = 2 is the order of
square matrices A and B In general, if A = kB where A and B are square matrices of order n, then | A| = kn
| B |, where n = 1, 2, 3
Example 3 Evaluate the determinant  ∆ = 
1
2
4
–1
3
0
4
1
0 Solution Note that in the third column, two entries are zero So expanding along third
column (C3), we get
∆ =
–1
3
1
2
1
2
4
– 0
0
4
1
4
1
–1
3
+
= 4 (–1 – 12) – 0 + 0  = – 52
Example 4 Evaluate ∆ = 
0
sin
–cos
–sin
0
sin
cos
–sin
0
α
α
α
β
α
β