Rows of a Matrix is divisible by 19, show that its Determinant is also divisible by 19
40538
On determinants and common divisors
2609
Is there a quick way to find the remainder when this determinant is divided by $5$?
4998
Question on determinants of matrices changing between integer matrices
134244
Determinant of a matrix will all off-diagonal elements equal
52564
$m\times n$ matrix with an even number of 1s in each row and column
78224
Suppose $A$ is a general $n \times n$ matrix and $B$ is obtained by interchanging two rows of $A$. Prove that $\det(B) = -\det(A)$
153961
Determinant of $2 \times 2$ block matrix with commuting blocks
125889
Determinant of rank-one perturbations of (invertible) matrices
113169
Number of $\pm 1$ matrices whose determinant is negative or zero
127085
Bound on the difference of two determinants
116376
Prove the determinant is the product of its diagonal entries
82925
Let the matrix $A=[a_{ij}]_{n×n}$ be defined by $a_{ij}=\gcd(i,j )$. How prove that $A$ is invertible, and compute $\det(A)$?
9574
How to show that $\det(AB) =\det(A) \det(B)$?
98646
Show determinant of matrix is non-zero
15452
Proving determinant product rule combinatorially
35015
Why must the determinant of a matrix with with integer entries be an integer?
98135
Show that the determinant of $A$ is equal to the product of its eigenvalues