In obtaining the solution of the system of equations x + y + z = 7 x + 2y + 3z = 16 and x + 3y + 4z = 22 by Cramer's rule, the value of y is obtained by dividing D by $D_{2}$ where 
$D=\left|\begin{matrix}1&1&1\\ 1&2&3\\ 1&3&4\end{matrix}\right|$ What is the value of the determinant $D_{2}$ ?

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?

Let 1, ω, $\omega ^ 2$ be three cube roots of unity. If x = a + b $y=a\omega +b\omega ^{2}, z=a\omega ^{2}+b\omega$ then what is $ x ^ 2 + y ^ 2 + z ^ 2$ equal to?