How to prove that if the determinant of the matrix is zero then at least one eigenvalue must be zero?
52208
Show that a matrix $A$ is singular if and only if $0$ is an eigenvalue.
125889
Determinant of rank-one perturbations of (invertible) matrices
152932
Proof: $\det\pmatrix{\langle v_i , v_j \rangle}\neq0$ $\iff \{v_1,\dots,v_n\}~\text{l.i.}$
113169
Number of $\pm 1$ matrices whose determinant is negative or zero
26793
What is the maximum possible value of determinant of a matrix whose entries either 0 or 1?
105988
Find the uniform lower bound of the smallest eigenvalue of a certain matrix
116539
Eigenvalues of matrix satisfying $A^2 = A$
74341
Proving an invertible matrix which is its own inverse has determinant $1$ or $-1$
41932
Prove that $\lambda = 0$ is an eigenvalue if and only if A is singular.
37537
Show that $det(A)=0$ for a Matrix $A$ Such That for $X=[2,3,4]^{T}$, $AX=0$
16439
What are the eigenvalues of matrix that have all elements equal 1?
18297
Suppose that each of the row sums of an $n\times n$ matrix $A$ is equal to zero. Show that $A$ must be singular.
149916
Minimum eigenvalue and singular value of a square matrix
22222
Properties of zero-diagonal symmetric matrices
135316
A basic question on diagonalizability of a matrix
125569
Prove that the eigenvalues of a real symmetric matrix are real
134244
Determinant of a matrix will all off-diagonal elements equal