Let $A$ be a $n \times n$ matrix such that $A$ is an upper-triangular matrix. Then $adj(A) =$

Let $A = (a_{ij})_{1 \leq i, j \leq 3}$ be a $3 \times 3$ invertible matrix where each $a_{ij}$ is a real number. Denote the inverse of the matrix $A$ by $A^{-1}$. If $\sum_{j=1}^3 a_{ij} = 1$ for $1 \leq i \leq 3$,then:

Let $A$ be a $4 \times 4$ matrix and $P$ be its adjoint matrix. If $|P|=\left|\frac{A}{2}\right|$,then $\left|A^{-1}\right|=$

If $A=\begin{bmatrix} \frac{1}{\sqrt{5}} & \frac{2}{\sqrt{5}} \\ \frac{-2}{\sqrt{5}} & \frac{1}{\sqrt{5}} \end{bmatrix}$,$B=\begin{bmatrix} 1 & 0 \\ i & 1 \end{bmatrix}$,$i=\sqrt{-1}$,and $Q=A^{T}BA$,then the inverse of the matrix $AQ^{2021}A^{T}$ is equal to:

Find the inverse of the matrix (if it exists): $\left[\begin{array}{lll}1 & 2 & 3 \\ 0 & 2 & 4 \\ 0 & 0 & 5\end{array}\right]$

If $A=\left[\begin{array}{ll}2 & 3 \\ 1 & 2\end{array}\right]$ and $B=\left[\begin{array}{cc}2 & -3 \\ -1 & 2\end{array}\right]$,then $\left(B^{-1} A^{-1}\right)^{-1}=$