query: Is $\rm\det (A+B) = \det (A) + \det (B)$?
positive_passages.docid: 125348
positive_passages.text: Does $\det(A + B) = \det(A) + \det(B)$ hold?
negative_passages.docid: 81818
negative_passages.text: Prove or disprove : $\det(A^k + B^k) \geq 0$
negative_passages.docid: 17394
negative_passages.text: Sign of determinant when using $det A^\top A$
negative_passages.docid: 51800
negative_passages.text: We have matrix $A\in M_{n-1\times n}(\mathbb Z)$ so that the sum of entries in each row is zero. Prove that $\det(AA^T)=nk^2.$
negative_passages.docid: 18964
negative_passages.text: Find the determinant of $I + A$
negative_passages.docid: 46825
negative_passages.text: The identity det(A) = exp(Tr(ln(A)) for A general
negative_passages.docid: 139534
negative_passages.text: Derivative of determinant, which is correct?
negative_passages.docid: 45261
negative_passages.text: Why is the determinant of a rotation matrix equal to 1?
negative_passages.docid: 71442
negative_passages.text: How to prove $\det(I+uv^\intercal)=1+v^\intercal u$
negative_passages.docid: 134402
negative_passages.text: $\mathrm{rank}(A)+\mathrm{rank}(I-A)=n$ for $A$ idempotent matrix
negative_passages.docid: 63920
negative_passages.text: Does the fact that matrices $A, B$ are similar imply that $A+cI$ is similar to $B+cI$?
negative_passages.docid: 83475
negative_passages.text: Prove Or Disprove: tr(AB)=tr(A)*tr(B)
negative_passages.docid: 109312
negative_passages.text: How is the matrix identity $\det\begin{pmatrix}A&B\\B&A\end{pmatrix}=\det(A+B)\det(A-B)$ proved?
negative_passages.docid: 125030
negative_passages.text: Prove that $\det(A)=p_1p_2-ba={bf(a)-af(b)\over b-a}$
negative_passages.docid: 32487
negative_passages.text: Proving $\det \left( \begin{smallmatrix} A & -B \\ B & A \end{smallmatrix} \right) =|\det(A+iB)|^2$
negative_passages.docid: 67784
negative_passages.text: If $A + A^t = 2I$ then $\det(A) \geq 1$
negative_passages.docid: 129647
negative_passages.text: $A^{-1}$ has integer entries if and only if the ${\rm det}\ (A) =\pm 1$