Matrices Test -...

If $$ \begin{bmatrix} 1/25 & 0 \\ x & 1/25 \end{bmatrix}\quad =\quad \begin{bmatrix} 5 & 0 \\ -a & 5 \end{bmatrix}^{ -2 } $$, then the value of x is 

The matrix $$\begin{bmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4 \end{bmatrix}$$ is a 

If $$A=\dfrac { 1 }{ \pi  } \begin{bmatrix} \sin ^{ -1 }{ \left( x\pi  \right)  }  & \tan ^{ -1 }{ \left( \dfrac { x }{ \pi  }  \right)  }  \\ \sin ^{ -1 }{ \left( \dfrac { x }{ \pi  }  \right)  }  & \cot ^{ -1 }{ \left( \pi x \right)  }  \end{bmatrix} B=\begin{bmatrix} -\cos ^{ -1 }{ \left( x\pi  \right)  }  & \tan ^{ -1 }{ \left( \dfrac { x }{ \pi  }  \right)  }  \\ \sin ^{ -1 }{ \left( \dfrac { x }{ \pi  }  \right)  }  & -\tan ^{ -1 }{ \left( \pi x \right)  }  \end{bmatrix}$$ then $$A-B$$ equal to

If matrix $$A=[a_{ij}]_{2\times 2}$$, where $$a_{ij} *1$$ if $$1*j$$ and $$0$$ if $$i=j$$ then $$A^2$$ is equal to

If $$A$$ and $$B$$ are square matrices of the same order, then $$(A+B)(A-B)$$ is equal to 

If $$A=\begin{bmatrix} 2 & 1 & 3 \\ 4 & 5 & 1 \end{bmatrix}$$ and $$B=\begin{bmatrix} 2 & 3 \\ 4 & 2 \\ 1 & 5 \end{bmatrix}$$, then 

If $$3\begin{bmatrix}2 & 3\\ -4 & 1\end{bmatrix} - 2 \begin{bmatrix} x& y\\ 3 & 4\end{bmatrix} = \begin{bmatrix}10 & 11\\ z & -5\end{bmatrix}$$, then $$x + y - z =$$

If the matrix $$A = \begin{bmatrix}2 & 0 & 0 \\ 0 & 2 & 0 \\ 2 & 0 & 2\end{bmatrix}$$, then $$A^n=\begin{bmatrix}a & 0 & 0 \\ 0 & a & 0 \\ b & 0 & a\end{bmatrix}. n \in N$$ where

$$A $$ is of order $$m \times n$$ and $$B$$ is of order $$p \times q,$$ addition of $$A$$ and $$B$$ is possible only if

What is the inverse of the matrix
$$A=\begin{bmatrix} \cos { \theta  }  & \sin { \theta  }  & 0 \\ -\sin { \theta  }  & \cos { \theta  }  & 0 \\ 0 & 0 & 1 \end{bmatrix}$$ ?