### Instruction: If $\det \mathbf{A} = 5,$ then find $\det (\mathbf{A^3}).$.### Response: I recall that the determinant of a matrix is a scalar that measures the area or volume of the parallelogram or parallelepiped spanned by its columns.
I also remember that the determinant has some nice properties, such as $\det (\mathbf{AB}) = \det (\mathbf{A}) \det (\mathbf{B})$ for any square matrices $\mathbf{A}$ and $\mathbf{B}.$