query: $\det{\begin{bmatrix} A & B \\ C & D\end{bmatrix}}=(D-1)\det(A) +\det(A-BC) $?
positive_passages.docid: 20331
positive_passages.text: Determinant of a $2\times 2$ block matrix
negative_passages.docid: 52973
negative_passages.text: The identity $(u\times v)\cdot(x\times y)=\begin{vmatrix}u\cdot x&v\cdot x\\ u\cdot y&v\cdot y\\\end{vmatrix}$
negative_passages.docid: 11557
negative_passages.text: How to prove $\det(e^A) = e^{\operatorname{tr}(A)}$?
negative_passages.docid: 517
negative_passages.text: Determinant of a specially structured matrix ($a$'s on the diagonal, all other entries equal to $b$)
negative_passages.docid: 85167
negative_passages.text: When A and B are of different order given the $\det(AB)$,then calculate $\det(BA)$
negative_passages.docid: 106619
negative_passages.text: Determinant of matrix
negative_passages.docid: 46825
negative_passages.text: The identity det(A) = exp(Tr(ln(A)) for A general
negative_passages.docid: 72578
negative_passages.text: Determinant value of a square matrix whose each entry is the g.c.d. of row and column position
negative_passages.docid: 142980
negative_passages.text: If $\,A^k=0$ and $AB=BA$, then $\,\det(A+B)=\det B$
negative_passages.docid: 45261
negative_passages.text: Why is the determinant of a rotation matrix equal to 1?
negative_passages.docid: 18964
negative_passages.text: Find the determinant of $I + A$
negative_passages.docid: 84775
negative_passages.text: How to evaluate $\det (1+x_iy_j)_{n\times n}$?
negative_passages.docid: 55062
negative_passages.text: $2\times 2$ matrix $C=AB-BA$
negative_passages.docid: 91028
negative_passages.text: determinant of a matrix with binomial coefficient entries
negative_passages.docid: 79031
negative_passages.text: Determinant of the Kronecker Product of Two Matrices
negative_passages.docid: 101040
negative_passages.text: Prove the equality: $\det\left[\begin{smallmatrix} -2a &a+b &a+c \\ b+a&-2b &b+c \\ c+a&c+b &-2c \end{smallmatrix}\right] = 4(a+b)(b+c)(c+a)$
negative_passages.docid: 37537
negative_passages.text: Show that $det(A)=0$ for a Matrix $A$ Such That for $X=[2,3,4]^{T}$, $AX=0$