Why is it that a matrix that is not invertible cant be expressed as a product of elementary matricies
114271
Why is a matrix invertible if it can be written as the product of elementary matrices?
123808
How would I solve the following problem involving elementary matrices?
141922
Reason for reversing the order when transpose and inverse of a group of matrices
84626
Why in these matrices are $AB=BA$ not equal? What is the logic behind them?
18465
Sum and product of two transcendental numbers can't be both algebraic
155272
Is a matrix with $1$s in the diagonal and off-diagonal entries with absolute value less than $1$ invertible?
21571
Why are real symmetric matrices diagonalizable?
33355
Proving that matrix in equation is invertible
26764
Proving that $\mathbb R^3$ cannot be made into a real division algebra (and that extending complex multiplication would not work)
112353
Prove that all 2x2 orthogonal matrices can be expressed as Rotation or Reflection
25682
If $A$ is an $m\times n$ matrix, $B$ is an $n\times m$ matrix and $n<m$, then $AB$ is not invertible.
21992
Examples proving why the tensor product does not distribute over direct products.
63475
Is there any connection between a matrix being invertible and being diagonalizable?
4517
Showing a $2\times2$ matrix is invertible
80623
Must $S$ be a unitary matrix?
18585
Showing $A-I$ is invertible, when $A$ is a skew-symmetric matrix
25159
Why does the inverse of the Hilbert matrix have integer entries?