### Instruction: If $\det \mathbf{A} = -1,$ then find $\det (\mathbf{7A}).$.### Response: I know that $\det (\mathbf{cA}) = c^n \det \mathbf{A}$ for any scalar $c$ and any $n \times n$ matrix $\mathbf{A}.$
In this case, I assume that $\mathbf{A}$ is also an $n \times n$ matrix, so $\det (\mathbf{7A}) = 7^n \det \mathbf{A}.$
Since $\det \mathbf{A} = -1,$ I can substitute that into the formula and get $\det (\mathbf{7A}) = 7^n (-1).$
This is the final answer, and it depends on the value of $n.$