Prove determinant of $n \times n$ matrix is $(a+(n-1)b)(a-b)^{n-1}$?
517
Determinant of a specially structured matrix ($a$'s on the diagonal, all other entries equal to $b$)
129743
$A$ be a $2\times 2$ real matrix with trace $2$ and determinant $-3$
48658
Let $A$ and $B$ be $n\times n$ matrices. Suppose $A$ is similar to $B$. Prove trace($A$) = trace($B$).
17430
If $\operatorname{rank}\left( \begin{bmatrix} A &B \\ C &D \end{bmatrix}\right)=n$ prove that $\det(AD)=\det(BC)$
110200
Determinant of a Special Symmetric Matrix
115582
Prove that if a product$ AB$ of $n\times n$ matrices is invertible, so are the factors $A$ and $B$.
144221
Matrix determinant lemma with adjugate matrix
113518
Determinant of the inverse matrix
146438
Determinant of a special skew-symmetric matrix
152932
Proof: $\det\pmatrix{\langle v_i , v_j \rangle}\neq0$ $\iff \{v_1,\dots,v_n\}~\text{l.i.}$
133449
A proof that an orthogonal matrix with a determinant 1 is a rotation matrix
104575
Formula for determinant of block matrix with commuting blocks
142363
The determinant of a block Matrix of Order $2n$
115905
The determinant of block triangular matrix as product of determinants of diagonal blocks
8554
Proof: $\mathrm{adj}(\mathrm{adj}(A)) = (\mathrm{det}(A))^{n-2} \cdot A$ for $A \in \mathbb{R}^{n\times n}$
90982
How to find the determinant of this $3 \times 3$ Hankel matrix?
38428
How tot start proving $A \times B \times C \ne (A \times B) \times C$?