If matrices $A$ and $B$ are orthogonal then $A-B$ or $A+B$ are singular
128990
Prove that, at least one of the matrices $A+B$ and $A-B$ has to be singular
24809
For all square matrices $A$ and $B$ of the same size, it is true that $(A+B)^2 = A^2 + 2AB + B^2$?
73677
If the matrix $A^3 = 0$, is $A$ singular?
149219
If $A$ is a non-square matrix with orthonormal columns, what is $A^+$?
29454
A and B are real, symmetric and positive semi-definite matrices of the same order; is AB diagonalizable?
141173
Are there matrices such that $AB=I$ and $BA \neq I$
114250
If $V_0$ is the subspace of matrices of the form $C=AB-BA$ for some $A,B$ in a vector space $V$ then $V_0=\{A\in V|\operatorname{Trace} (A)=0\}$
33542
When is $A- B = B- A$?
38436
If an orthogonal matrix has determinant -1 then it has -1 as an eigenvalue
37794
Proving the two given vectors are orthogonal
43570
Finding two non-zero matrices where $AX = BA$
112353
Prove that all 2x2 orthogonal matrices can be expressed as Rotation or Reflection
89729
If $X$ is a singular matrix, then is $X'X$ singular?
33560
Show that matrices $A$ and $B$ commute if and only if $\begin{vmatrix} b & a-c \\ e & d-f\end{vmatrix}=0.$
37985
Show that $|x|^2 = |y|^2$ with $A$ orthogonal and $Ax = \cos (θ)x − \sin (θ)y$, $Ay = \sin (θ)x + \cos (θ) y$
14189
If $(I-A)(I+A)^{-1}$ is orthogonal then prove that A is skew symmetric.
66500
Proving that orthogonal vectors are linearly independent