Consider the real matrices $$A = \left( \begin{array} { c c c }
1 & - 1 & k \\
k & 1 & - 1
\end{array} \right) , \quad B = \left( \begin{array} { c c }
1 & 1 \\
1 & - 1 \\
1 & 0
\end{array} \right)$$ a) (1 point) Calculate for which values of the parameter $k$ the matrix AB has an inverse. Calculate the inverse matrix of AB for $k = 1$. b) (1 point) Calculate BA and discuss its rank as a function of the value of the real parameter $k$. c) ( 0.5 points) In the case $k = 1$, write an inconsistent system of three linear equations with three unknowns whose coefficient matrix is BA.
Consider the real matrices
$$A = \left( \begin{array} { c c c }
1 & - 1 & k \\
k & 1 & - 1
\end{array} \right) , \quad B = \left( \begin{array} { c c }
1 & 1 \\
1 & - 1 \\
1 & 0
\end{array} \right)$$
a) (1 point) Calculate for which values of the parameter $k$ the matrix AB has an inverse. Calculate the inverse matrix of AB for $k = 1$.\\
b) (1 point) Calculate BA and discuss its rank as a function of the value of the real parameter $k$.\\
c) ( 0.5 points) In the case $k = 1$, write an inconsistent system of three linear equations with three unknowns whose coefficient matrix is BA.