How is the determinant of a 3x3 matrix denoted?

In linear algebra, the determinant of a 3x3 matrix can be denoted in more than one common way. The notations det(A) and |A| are standard and widely accepted.

The notation det(A) explicitly indicates that we are discussing the determinant of matrix A. This form is particularly useful when context requires clarity or when working with multiple matrices, as it unmistakably communicates that the determinant is being referenced.

On the other hand, the vertical bars notation |A| serves as a shorthand that also signifies the determinant of matrix A. This notation is often preferred in more compact mathematical expressions or when the context is clear enough that there is no ambiguity.

Both notations are valid and interchangeable, making them equally common in mathematical writing. Thus, the most comprehensive answer acknowledges both notations, which is why the chosen answer confirms that both forms are acceptable representations of the determinant of a 3x3 matrix.