FAQs

Q1: Can determinants be calculated for non-square matrices?

A1: No, determinants can only be calculated for square matrices, i.e., matrices with an equal number of rows and columns.

Q2: Are determinants commutative under multiplication?

A2: No, determinants are not commutative under multiplication. In general, det(AB) is not equal to det(A) * det(B).

Q3: How are determinants used in solving systems of equations?

A3: For a system of linear equations, the determinant of the coefficient matrix helps determine whether the system has a unique solution, no solution, or infinite solutions.

Q4: What does a determinant of zero indicate for a matrix?

A4: A determinant of zero indicates that the matrix is singular, and its columns (or rows) are linearly dependent.

Q5: Can determinants be negative?

A5: Yes, determinants can be negative, positive, or zero, depending on the arrangement of elements in the matrix.