Solution of $$x-y+z=4 ; x-2 y+2 z=9$$ and $$2 x+y+3 z=1$$ is

If for any 2 $$\times$$ 2 square matrix A,

A (adj A) = $$\left[ {\matrix{ 8 & 0 \cr 0 & 8 \cr } } \right]$$, then find the value of det (A).

If $$A = \left[ {\matrix{ a & 0 & 0 \cr 0 & a & 0 \cr 0 & 0 & a \cr } } \right]$$, then $$|A||adj\,A|$$ is equal to

If $$A = \left[ {\matrix{ {2 - k} & 2 \cr 1 & {3 - k} \cr } } \right]$$ is a singular matrix, then the value of $$5k - {k^2}$$ is