Using matrix algebra prove that $ \left = \left$
71064
How to prove that $\langle Av,w\rangle=\langle v,A^Tw\rangle$?
109312
How is the matrix identity $\det\begin{pmatrix}A&B\\B&A\end{pmatrix}=\det(A+B)\det(A-B)$ proved?
31149
Prove that matrix can be square of matrix with real entries
74341
Proving an invertible matrix which is its own inverse has determinant $1$ or $-1$
145352
How to prove $\sum_{d|n} {\tau}^3(d)=\left(\sum_{d|n}{\tau}(d)\right)^2$
153506
Proving the inverse of a matrix equals $I_n-\frac{1}{n-1}A$
5616
How can I prove the IFF condition for this group of matrices?
58491
Proving the inverse of a matrix as a polynomial of matrices
31999
Relation of this antisymmetric matrix $r = \left(\begin{smallmatrix}0 &1\\-1&0\end{smallmatrix}\right)$ to $i$
67820
Showing that $(A_{ij})=\left(\frac1{1+x_i+x_j}\right)$ is positive semidefinite
127127
Prove condition number of a invertible matrix is atleast one
102935
Trace and determinant of composition of a left-multiplication and a right-multiplication on a space of matrices
65783
Proving: "The trace of an idempotent matrix equals the rank of the matrix"
30882
Proving Invertibility and Eigenvalues
18914
How prove this $A=\left(B-\frac{1}{110}I\right)^T\left(B+\frac{1}{110}I\right)$
137920
Proving an equation with invertible matrices
55779
How to prove: $\left(\frac{2}{\sqrt{4-3\sqrt[4]{5}+2\sqrt[4]{25}-\sqrt[4]{125}}}-1\right)^{4}=5$?