### Instruction: If $\det \mathbf{A} = -1,$ then find $\det (\mathbf{7A}).$.### Response: To find the determinant of a scalar multiple of a matrix, I can use the property that $\det (k\mathbf{A}) = k^n \det (\mathbf{A})$, where $n$ is the size of the matrix.
In this case, $\mathbf{A}$ must be a square matrix, since it has a determinant, but I don't know its size.
However, I can use a variable to represent it, say $n \times n$, and apply the formula with $k = 7$.
Then, $\det (\mathbf{7A}) = 7^n \det (\mathbf{A})$.
Since I know that $\det \mathbf{A} = -1$, I can plug that in and simplify.
I get $\det (\mathbf{7A}) = 7^n (-1) = -7^n$.