Is it true that given a matrix $A$, $A$ has L.I columns/rows if and only if $\text {det}(A)\neq 0$?
4443
Why is the determinant zero iff the column vectors are linearly dependent?
103061
Why is it true that $\mathrm{adj}(A)A = \det(A) \cdot I$?
23847
Determinant of a matrix whose $(i,j)$th element is $|i-j|$?
51800
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 $\det(AA^T)=nk^2.$
140252
Matrices - Conditions for $AB+BA=0$
35015
Why must the determinant of a matrix with with integer entries be an integer?
64517
Prove that row rank of a matrix equals column rank
106305
Prove/disprove: if $\det(A+X) = \det(B + X)$ for all $X$, then $A=B$
9250
Can the zero vector be an eigenvector for a matrix?
84341
Can the determinant of a matrix can be made $0$?
75104
Existence of some type matrix
17430
If $\operatorname{rank}\left( \begin{bmatrix} A &B \\ C &D \end{bmatrix}\right)=n$ prove that $\det(AD)=\det(BC)$
129647
$A^{-1}$ has integer entries if and only if the ${\rm det}\ (A) =\pm 1$
155884
What are the conditions on $\text{tr}(AB) \leq \text{tr(A)} \text{tr(B)}$ to be true?
69980
Proving that if $A$ is an $n\times n$ orthogonal matrix, then $\det(A) = \pm1$
102707
Why square matrix with zero determinant have non trivial solution
106398
If $A$ is invertible show that $\det(A) \neq 0$