Linear Algebra

If $a + b + c \neq 0$, the system of equations: $(b+c)(y+z) - ax = b - c$ $(c+a)(z+x) - by = c - a$ $(a+b)(x+y) - cz = a - b$ has:

If $A=\begin{bmatrix} 1 &0 &0 \\ 0& 1 &1 \\ 0&-2 & 4 \end{bmatrix}$ and $6A^{–1} = A^{2} + cA + dI$, where $A^{–1}$ is A- inverse, I is the identify matrix, then (c, d) is

Suppose, the system of linear equations 

If $A=\begin{bmatrix} a &b &c \\ b & c & a\\ c& a &b \end{bmatrix}$ , where $a, b, c$ are real positive numbers such that $abc = 1$ and $A^{T}A=I$ then the equation that not holds true among the following is