A matrix is simply an ordered arrangement of elements; it is meaningless to assign a single numerical value to matrix.

However, if A is a square matrix, then the determinant function as-societies with A exactly one numerical value called the determinant of A. Denoting the determinant of A by |A| (that is, using vertical bars) we can think of the determinant function as a correspondence:

     A                 →                |A|
square matrix             determinant of A

The determinant has a variety of uses, but first we need to find out how determinant may be evaluated.

Definition. (Determinant of order 1) Let A = [a₁₁] be a square matrix of order 1. Then determinant of A is defined as the number a₁₁ itself. That is,  |a₁₁| = a₁₁.

Example. |3| = 3,  |-5| = -5  and |0| = 0.

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