2 2  Determinant of a matrix of order two
Let
A = 
11
12
21
22
a
a
a
a






 be a matrix of order 2 × 2,
then the determinant of A is defined as:
det (A) = |A| = ∆ = 
 = a11a22 – a21a12
Example 1 Evaluate 
2
4
–1
2 Solution We have 
2
4
–1
2  = 2(2) – 4(–1) = 4 + 4 = 8 Example 2 Evaluate 
1
x– 1
x
x
x
+
Solution We have
1
x– 1
x
x
x
+
 = x (x) – (x + 1) (x – 1)  = x2 – (x2 – 1) = x2 – x2 + 1 = 1
4