Introduction
In a 2×2 square matrix, the determinant is obtained by subtracting the product of the elements of the secondary diagonal by the product of the elements of the leading diagonal.
Determinant of a matrix is written as |A| or |A+B| or |B|. The name of the the matrix should be written inside ‘||’.
In a 1×1 square matrix, determinant is the same element in the matrix. i.e. A = [a] and |A| = a.
Important:
The determinant is defined only for square matrices. A matrix having an equal number of rows and columns is said to be a square matrix. The order of such a matrix is mxm.
Determinant of 2×2 Matrix
Let us consider a square matrix A of order 2×2 whose elements are as follows:
$\text{A} = \left [ \displaylines{ a & b \\ c & d} \right ] _{2×2}$
The determinant of matrix A, denoted by |A| is defined by
$\text{|A|} = \left | \displaylines{ a & b \\ c & d} \right | = (ad – bc)$
Solved Examples
Example 1. If $\text{A} = [a]$, what is the value of |a|?
Solution:
Given,
$\text{A} = [a]$
Now,
Determinant of matrix A = |a| = a
Example 2: If $\text{A} = \left [ \displaylines{1 & 2 \\ 3 & 4} \right ]_{2×2}$, find the value of determinant of A.
Solution:
Given,
$\text{A} = \left [ \displaylines{ 1 & 2 \\ 3 & 4} \right ] _{2×2}$
Now,
$\text{|A|} = \left | \displaylines{1 & 2 \\ 3 & 4 } \right ]_{2×2}$
$= (1 * 4 – 2 * 3)$
$= 4 – 6$
$= -2$
Therefore, the required value of determinant of A is -2.