If A is an invertible matrix of order 2, then $\det(( {adj } A)^{-1})$ is equal to

If the points (a₁, b₁), (a₂, b₂) and (a₁ + a₂, b₁ + b₂) are collinear, then

If A and B are invertible matrices of the same order, then $(AB)^{-1}$ is equal to

The value of $\begin{vmatrix} 1 & bc & bc(b+c) \\ 1 & ca & ca(c+a) \\ 1 & ab & ab(a+b) \end{vmatrix}$ is

If A and B are two square symmetric matrices of same order, then AB-BA is

If $(AB)^T = C$, where $A = \begin{bmatrix} x & -1 \\ 2 & 3 \end{bmatrix}$, $B = \begin{bmatrix} 4 & 5 \\ 1 & -2 \end{bmatrix}$ and $C = \begin{bmatrix} 3 & 11 \\ 7 & y \end{bmatrix}$, then $x+y$ is :

if $A = \begin{bmatrix}1 & 0\\3 & 1\end{bmatrix}$ and $A^4 = \begin{bmatrix}1 & 0\\k & 1\end{bmatrix}$ then value of $k$ is