Determinants Te...

If $$A=\begin{bmatrix} 2 & -3 \\ -4 & 1 \end{bmatrix}$$, then $$adj(3A^{2}+12A)$$ is equal to:

$$P = \left[ {\begin{array}{*{20}{c}}1&\alpha &3\\1&3&3\\2&4&4\end{array}} \right]$$ is the adjoint of a $$3 \times 3$$ matrix A and $$\left| A \right| = 4,$$ then $$\alpha $$ is equal to 

If  $$A = \left( \begin{array} { l l } { 1 } & { 2 } \\ { 3 } & { 5 } \end{array} \right), $$  then the value of the determinant  $$\left| A ^ { 2009 } - 5 A ^ { 2008 } \right|$$  is

The adjoining of the matrix $$\begin{bmatrix} 1 & -2 & 3 \\ 0 & 2 & -1 \\ -4 & 5 & 2 \end{bmatrix}$$, is 

There are 12 points in a plane of which 5 are collinear. The maximum number of distinct quadrilaterals which can be formed with vertices at these points is 

If $$A=A=\left[ \begin{matrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a \end{matrix} \right]$$,then $$\left| A \right| \left| AdjA \right|$$ is equal to

If $$A=\begin{bmatrix} { a }_{ 1 } & { a }_{ 2 } & { a }_{ 3 } \\ { b }_{ 1 } & { b }_{ 2 } & { b }_{ 3 } \\ { c }_{ 1 } & { c }_{ 2 } & { c }_{ 3 } \end{bmatrix}$$ and $$A_i,B_i,C_i$$ are cofactors of $$a_i,b_i,c_i$$ then $$a_1B_1+a_2B_2+a_3B_3=$$

If $$A$$ is a square matrix $$(adj \,A)' - (adj \,A')$$

If $$A$$ is singular matrix, then $$A.(adj\,A)$$ is 

Let $${\Delta _{\text{o}}} = $$ $$\left[ \begin{matrix} { a }_{ 11 } & { a }_{ 12 } & { a }_{ 13 } \\ { a }_{ 21 } & { a }_{ 22 } & { a }_{ 23 } \\ { a }_{ 31 } & { a }_{ 32 } & { a }_{ 33 } \end{matrix} \right] $$ and let $${\Delta _1}$$ denote the determinant formed by the cofactors of elements of $${\Delta _0}$$ and $${\Delta _2}$$ denote the determinant formed by the cofactor of $${\Delta _1},$$ similarly $${\Delta _n}$$ denotes the determinant formed by the cofactors of $${\Delta _{n - 1}}$$ then the determinant value of $${\Delta _n}$$ is