Matrices Test -...

If $$A=\left[ \begin{matrix} 6 & 9 \\ -4 & -6 \end{matrix} \right] $$, then $$A^{2}$$=

If the order of $$A$$ is $$4 \times 3$$, the order of $$B$$ is $$4 \times 5$$ and the order of $$C ,\ 7\times 3$$ then the order of $$(A^{T}B^{T})^{T}C^{T}$$ is

The inverse of a symmetric matrix is

If $$\left[ \begin{matrix} a \\ 8 \end{matrix}\begin{matrix} 5 \\ b \end{matrix} \right]$$ $$-$$ $$\left[ \begin{matrix} 4 \\ 7 \end{matrix}\begin{matrix} 6 \\ 2 \end{matrix} \right]$$ =$$\left[ \begin{matrix} 2 \\ 1 \end{matrix}\begin{matrix} -1 \\ 5 \end{matrix} \right],$$ then value of $$a$$ is

If $$A=\left[ \begin{matrix} 1 & 0 & -1 \\ 3 & 4 & 5 \\ 0 & 6 & 7 \end{matrix} \right]$$ and $$A^{-1}=[\alpha_{ij}]_{3\times 3}$$ then $$\alpha_{23}=$$

If $$A=\begin{bmatrix} 2 & -1 \\ -1 & 2 \end{bmatrix}$$ and $$I$$ is the unit matrix of order $$2$$, then $$A^{2}$$ equals 

If $$\begin{bmatrix} 3 & 2 & -1 \\ 4 & 9 & 2 \\ 5 & 0 & -2 \end{bmatrix}\begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 0 \\ 7 \\ 2 \end{bmatrix}$$, then $$(x,\ y,\ z)=$$ 

If A is a 2 X 2 matrix such that $$A^{2009} + A^{2008}$$= I, then : $$(A^{2008})^{-1}$$= 

If $$\left[ \begin{matrix} 2 & -3 \\ 1 & \lambda  \end{matrix} \right] \times \left[ \begin{matrix} 1 & 5 & \mu  \\ 0 & 2 & -3 \end{matrix} \right] =\left[ \begin{matrix} 2 & 4 & 1 \\ 1 & -1 & 13 \end{matrix} \right],$$ then

Let p be a non-singular matrix, $$1+p+p^{2}+....+p^{n}=0$$ (0 denotes the null matrix) then $$p^{-1}=$$