Prove the following equalities about matrices
90486
If $(A-B)^2=O_2$ then $\det(A^2 - B^2)=(\det(A) - \det(B))^2$
95677
Linear Matrix Inequality of a matrix $T$ with $\| T \|_2 < \rho$
94639
Proof that the rank of a skew-symmetric matrix is at least $2$
64517
Prove that row rank of a matrix equals column rank
158845
Given $A$ and $B$ positive-definite matrices and $Q$ unitary matrix, prove that if $A = BQ$, then $A=B$.
29788
Eigenvalues of a matrix whose square equals its transpose
32487
Proving $\det \left( \begin{smallmatrix} A & -B \\ B & A \end{smallmatrix} \right) =|\det(A+iB)|^2$
120867
How prove this two symmetric matrices $AB=0$
19203
Is the rank of a matrix the same of its transpose? If yes, how can I prove it?
117175
Proof that the 2-norm of orthogonal transformation of a matrix is invariant
88746
Positive definiteness of the matrix $A+B$
86940
Proving an inequality in Eigenvalues of a matrix
123808
How would I solve the following problem involving elementary matrices?
76335
Proving that two matrices are congruent, in order to establish a rank and signature result.
54740
Proofs of Determinants of Block matrices
109217
Invertibility of the Product of Two Matrices
125569
Prove that the eigenvalues of a real symmetric matrix are real