query: How can I prove that the determinant of the matrix is $0$ only when $a=b=c=d=0$?
positive_passages.docid: 61580
positive_passages.text: Calculating the determinant gives $(a^2+b^2+c^2+d^2)^2$?
negative_passages.docid: 156761
negative_passages.text: If $p+q+r=0$, find the value of the determinant
negative_passages.docid: 142957
negative_passages.text: How to evaluate the determinant
negative_passages.docid: 98646
negative_passages.text: Show determinant of matrix is non-zero
negative_passages.docid: 110200
negative_passages.text: Determinant of a Special Symmetric Matrix
negative_passages.docid: 93903
negative_passages.text: What is the determinant of cofactor matrix of a matrix?
negative_passages.docid: 45261
negative_passages.text: Why is the determinant of a rotation matrix equal to 1?
negative_passages.docid: 51321
negative_passages.text: Prove that $A = B = C = D$
negative_passages.docid: 7205
negative_passages.text: Find the determinant of $A + I$, where $A$ is a real matrix such that $AA^{\top}=I$ and $\det A<0$.
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: 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: 126769
negative_passages.text: Linear independence of columns implies non-zero determinant
negative_passages.docid: 142980
negative_passages.text: If $\,A^k=0$ and $AB=BA$, then $\,\det(A+B)=\det B$
negative_passages.docid: 58921
negative_passages.text: How to calculate the determinant of all-ones matrix minus the identity?
negative_passages.docid: 37537
negative_passages.text: Show that $det(A)=0$ for a Matrix $A$ Such That for $X=[2,3,4]^{T}$, $AX=0$
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: 33448
negative_passages.text: Proof if $AB+BA=0$ Then atleast one of the matrices are singular.