A is a square matrix of order 3 such that its determinant is 4. What is the determinant of its transpose?

Consider the following in respect of non-singular matrices A and B:

I. $(AB) ^ {- 1} = A ^ {- 1} B ^ {- 1}$

II. $ (BA)(AB)^{-1}=I$ = I where I is the identity matrix

III. $ (AB)^{T}=A^{T}B^{T} $

How many of the above are correct?

If

 $\begin{bmatrix} x & 1 & 1 \end{bmatrix} \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} \begin{bmatrix} 1 \\ 1 \\ x \end{bmatrix} = \begin{bmatrix} 45 \end{bmatrix}$

then which one of the following is a value of x?

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 $x{}^2+y{}^2+z{}^2$?