Why is it that when a determinant = 0 then the homogeneous equations represented by the matrix has a non trivial solution?
102707
Why square matrix with zero determinant have non trivial solution
156761
If $p+q+r=0$, find the value of the determinant
121767
Why $\det(A^{-1}) = 1/\det(A)$?
122801
Probability of having zero determinant
134244
Determinant of a matrix will all off-diagonal elements equal
120407
Is every noninvertible matrix a zero divisor?
98646
Show determinant of matrix is non-zero
70381
Find the determinant of a symmetric matrix
33448
Proof if $AB+BA=0$ Then atleast one of the matrices are singular.
73677
If the matrix $A^3 = 0$, is $A$ singular?
121358
What is the exact relation between a full rank matrix and its determinant?
4443
Why is the determinant zero iff the column vectors are linearly dependent?
113169
Number of $\pm 1$ matrices whose determinant is negative or zero
50870
What's an intuitive way to think about the determinant?
2271
Determinant of a rank $1$ update of a scalar matrix, or characteristic polynomial of a rank $1$ matrix
110484
Condition on a matrix so that its determinant is $2$
32071
General solution of linear equation = particular + general homogeneous solution