Determinants Te...

A= \begin{bmatrix} -1 & -2 & -2 \\ 2 & 1 & -2 \\ 2 & -2 & 1 \end{bmatrix} then Adj(A)=

If $$A=\begin{bmatrix} -4 & -1 \\ 3 & 1 \end{bmatrix}$$ then the determinant of the matrix $$\left( {A}^{2016}-2{A}^{2015}-{A}^{2014} \right) $$ is

There are  $$12$$  points in a plane. The number of the straight lines joining any two of them when  $$3$$  of them are collinear is.

If adj B = A, |P| = |Q| = 1, then adj $$\left( { Q }^{ -1 }{ BP }^{ -1 } \right) $$ is

If $$A$$ is $$4\times 4$$ matrix and if $$\left| \left| A \right| adj\left( \left| A \right| A \right)  \right| ={ \left| A \right|  }^{ n }$$, then $$n$$ is 

If $$A=\begin{bmatrix} 5a & -b \\ 3 & 2 \end{bmatrix}$$ and $$A(adj\, A)=A{A}^{T}$$ then $$5a+3b$$ is equal to 

Two straight lines intersects at a point O. Points $$A_1, A_2,....A_n $$ are taken on one line and $$B_1,B_2,....B_n $$  on the other. If the point O is not to be used, the number of triangles that can be drawn using these points as vertices, is:

If A and B are square matrices of order 3 such that $$\left | A \right | $$= -1,$$\left | B \right | $$=3, then $$\left | 3AB \right | $$ equals

If $$f'(x)=\begin{vmatrix} mx & mx-p & mx+p \\ n & n+p & n-p \\ mx+2n & mx+2n+p & mx+2n-p \end{vmatrix}$$, then $$y=f(x)$$ represents

Let $$ A=  \left[ \begin{matrix} 1 & 2 & 3 \\ 2 & 0 & 5 \\ 0 & 2 & 1 \end{matrix} \right]  $$ and $$ B =  \left[ \begin{matrix} 0 \\ -3 \\ 1 \end{matrix} \right]  $$ which of the following is true ?