If $$A$$ and $$B$$ are two matrices, such that $$A B=B$$ and $$B A=A$$, then $$A^2+B^2$$ equals to

If $$A=\left[\begin{array}{cc}2-k & 2 \\ 1 & 3-k\end{array}\right]$$ is singular matrix, then the value of $$5 k-k^2$$ is equal to

If $$\Delta=\left|\begin{array}{ccc}1 & a & a^2 \\ 1 & b & b^2 \\ 1 & c & c^2\end{array}\right|$$ and $$\Delta_1=\left|\begin{array}{ccc}1 & 1 & 1 \\ b c & c a & a b \\ a & b & c\end{array}\right|$$, then

If $$A=\left[\begin{array}{cc}1 & \tan \alpha / 2 \\ -\tan \alpha / 2 & 1\end{array}\right]$$ and $$A B=I$$, then $$B$$ is equal to