There are six ways of expanding a determinant of order
Rationalised 2023-24
 78
MATHEMATICS
3 corresponding to each of three rows (R1, R2 and R3) and three columns (C1, C2 and
C3) giving the same value as shown below Consider the determinant of square matrix A = [aij]3 × 3
i e ,
| A | =
21
22
23
31
32
33
a
a
a
a
a
a
11
12
13
a
a
a
Expansion along first Row (R1)
Step 1 Multiply first element a11 of R1 by (–1)(1 + 1) [(–1)sum of suffixes in a11] and with the
second order determinant obtained by deleting the elements of first row (R1) and first
column (C1) of | A | as a11 lies in R1 and C1,
i