Q3.

If \[ [\,x \;\; 1 \;\; 1\,] \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} \begin{bmatrix} 1 \\ 1 \\ x \end{bmatrix} = \begin{bmatrix} 45 \end{bmatrix} \] then which one of the following is a value of $x$? 

Q4.

If \[ A = \begin{bmatrix} y & z & x \\ z & x & y \\ x & y & z \end{bmatrix} \] where \( x, y, z \) are integers, is an orthogonal matrix, then what is the value of \( x^2 + y^2 + z^2 \)?

Q5.

Consider the following in respect of a non-singular matrix \( M \):

1. \( |M^2| = |M|^2 \)
2. \( |M| = |M^{-1}| \)
3. \( |M| = |M^T| \)

How many of the above are correct?