Matrices Test -...

If $A = \begin{bmatrix} 2& 0 & 0\\ 0 & 2 & 0\\ 0 & 0 & 2\end{bmatrix}$, then $A^6 =$

Least number of changes for the expression $ax^{2} + bxy + cy^{2} + dx + ey + f$ to be symmetric in x and y is

If $A = \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}$, $B = \begin{bmatrix} 1 & 0 \\ 0 & 0 \end{bmatrix}$, then $BA =$

If $A$ and $B$ are square matrices such that $AB = I$ and $BA = I$, then $B$ is

Consider the following statements in respect of the matrix $A = \begin{bmatrix} 0 & 1 & 2\\ -1 & 0  & -3 \\ -2 & 3 & 0 \end{bmatrix}$ :
1. The matrix A is skew-symmetric.
2. The matrix A is symmetric.
3. The matrix A is invertible.
Which of the above statements is/are correct ? 

If the sum of the matrices $\begin{bmatrix} x \\ x \\ y \end{bmatrix},\begin{bmatrix} y \\ y \\ z \end{bmatrix}$ and $\begin{bmatrix} z \\ 0 \\ 0 \end{bmatrix}$ is the matrix $\begin{bmatrix} 10 \\ 5 \\ 5 \end{bmatrix}$, then what is the value of  $y$?

If $[2\ 3\ 4] \begin{bmatrix}1 & x &3 \\ 2 & 4 & 5\\ 3 & 2 &x \end{bmatrix} \begin{bmatrix} x\\ 2 \\  0 \end{bmatrix} = 0$, then $x =$ ________.

If $A$ is any matrix, then the product $AA$ is defined only when A is a matrix of order $m \times n$ where : 

Consider the following statements:
1. The product of two non-zero matrices can never be identity matrix.
2. The product of two non-zero matrices can never be zero matrix.
Which of the above statements is/are correct?

What is $\begin{bmatrix} x & y & z \end{bmatrix} \begin{bmatrix} a& h & g\\ h & b & f\\ g & f & c\end{bmatrix}$ equal to?