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?