Yes, a matrix can have a fractional determinant. The determinant of a matrix is a scalar value that is calculated based on the elements of the matrix. It represents certain properties of the matrix, such as whether the matrix is invertible or singular.

  Determinants can be rational or irrational numbers, including fractions. In fact, the determinant of a matrix can be any real number. It is not limited to whole numbers or integers. This means that the determinant of a matrix can be a fraction, a decimal, or even an irrational number like √2 or π.

  For example, consider the following 2x2 matrix:

  | 1.5 0.5 |

  | 0.3 0.9 |

  To find the determinant of this matrix, we use the formula:

  det(A) = (1.5 * 0.9) - (0.5 * 0.3)

   = 1.35 - 0.15

   = 1.2

  Here, the determinant is 1.2, which is a fractional value.

  So, in conclusion, matrices can have fractional determinants. The determinant is a scalar that can be any real number, including fractions.