What is the adjoint of the matrix $$\left( {\matrix{ {\cos ( - \theta )} & { - \sin ( - \theta )} \cr { - \sin ( - \theta )} & {\cos ( - \theta )} \cr } } \right)$$ ?

What should be the value of x, so that the matrix $$\left( {\matrix{ 2 & 4 \cr { - 8} & x \cr } } \right)$$ does not have an inverse?

If $$A = \left( {\matrix{ 1 & 2 \cr 2 & 3 \cr } } \right)$$ and $${A^2} - kA - {I_2} = O$$, where I₂ is the 2 $$\times$$ 2 identity matrix, then what is the value of k?

What is the inverse of the matrix $$A = \left( {\matrix{ {\cos \theta } & {\sin \theta } & 0 \cr { - \sin \theta } & {\cos \theta } & 0 \cr 0 & 0 & 1 \cr } } \right)$$ ?