It equals 0 if and only if the matrix is non-invertible, and it equals 1 for an identity matrix.
This is the only alternating multilinear function, up to a constant factor. This function can be expressed in terms of the sign function of elements in the symmetric group, as in the Leibniz formula. Using the Laplace expansion, it can be computed via expansion by minors. This function appears in the formula for a characteristic polynomial, as well as in Cramer's rule. It equals 0 if and only if the matrix is non-invertible, and it equals 1 for an identity matrix. For 10 points, name this value associated with a square matrix, which for a 2 by 2 matrix is calculated as ad minus bc.
This is the only alternating multilinear function, up to a constant factor.
matrix {determinant}