A second order determinant involves four elements a , b, c and d which may

either be numbers (real or complex) or functions, and it is displayed by writing them as follows:

a b

c d


The value of this second order determinant is defined to be

a b

c d


Thus, by way of example, we have

3 2 4 5

35(2)4 23,

1 i 1 2 2 i

(1 i)(2 i)12 1 i,


x1 3 2 x2

(x1)(x2)23 x2x8:

More generally, an nth order determinant involves n2 elements arranged in

n rows and n columns. The order of the determinant is the number of ele-

ments (entries) in a row on a column. Equivalently, the order of a determi-

nant is the number of elements in the diagonal line drawn from top left to

bottom right in the determinant; this is called the leading diagonal. We use

the convention that the symbol aij represents the element in a determinant

which is located in the ith row and the jth column. Thus a32 represents the element in row 3 and column 2, while a14 represents the element in row 1 and

column 4. This convention is illustrated in the following diagram:

11 12 1n a21 a22 . . . a2n

an1 an2 . . . ann


with the elements a11, a22, . . . , ann comprising the leading diagonal.