For a matrix $\mathbf{M},$ the trace of $\mathbf{M}$ is defined as the sum of its diagonal elements.  For example,
\[\operatorname{Tr} \begin{pmatrix} a & b \\ c & d \end{pmatrix} = a + d.\]Given $\operatorname{Tr} (\mathbf{A}) = 2$ and $\operatorname{Tr} (\mathbf{A}^2) = 30,$ find $\det \mathbf{A}.$
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<|im_start|>user
For a matrix $\mathbf{M},$ the trace of $\mathbf{M}$ is defined as the sum of its diagonal elements.  For example,
\[\operatorname{Tr} \begin{pmatrix} a & b \\ c & d \end{pmatrix} = a + d.\]Given $\operatorname{Tr} (\mathbf{A}) = 2$ and $\operatorname{Tr} (\mathbf{A}^2) = 30,$ find $\det \mathbf{A}.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
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user
-13
For a matrix $\mathbf{M},$ the trace of $\mathbf{M}$ is defined as the sum of its diagonal elements.  For example,
\[\operatorname{Tr} \begin{pmatrix} a & b \\ c & d \end{pmatrix} = a + d.\]Given $\operatorname{Tr} (\mathbf{A}) = 2$ and $\operatorname{Tr} (\mathbf{A}^2) = 30,$ find $\det \mathbf{A}.$
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