Matrices: Determinant - Second Order

A determinant is a special set of mathematical operations associated with a square array. The result of the operation is a scalar value for a numerical array. This array may be part of a matrix The determinant is usually enclosed between a pair vertical bars. The simplest determinant is defined for a 2 x 2 array.  It is called a determinant of second order. There is difference between a determinant  and a matrix.  The determinant is associated with a defined set of arithmetic operations.

» A=[1 2; 3 4]    % define A
A =
     1     2
     3     4
» det(A)    % calculate determinant of A
ans =
    -2

» syms b11 b12 b21 b22  % define symbolic variables
» B=[b11 b12; b21 b22]    % define symbolic matrix B
B =
[ b11, b12]
[ b21, b22]
» det(B)        % calculate determinant - check definition
ans =
b11*b22-b12*b21