The adjoint of the matrix $$A = \left[ {\matrix{ 1 & 0 & 2 \cr 2 & 1 & 0 \cr 0 & 3 & 1 \cr } } \right]$$ is

If a, b, c are non-zero real numbers, then the inverse of the matrix $$A = \left[ {\matrix{ a & 0 & 0 \cr 0 & b & 0 \cr 0 & 0 & c \cr } } \right]$$ is equal to

If $$A = \left[ {\matrix{ {\cos \alpha } & {\sin \alpha } \cr { - \sin \alpha } & {\cos \alpha } \cr } } \right]$$, then what is AA^T equal to (where, A^T is transpose of A)?

$$A = \left[ {\matrix{ {x + y} & y \cr x & {x - y} \cr } } \right]$$, $$B = \left[ {\matrix{ 3 \cr { - 2} \cr } } \right]$$ and $$C = \left[ {\matrix{ 4 \cr { - 2} \cr } } \right]$$. If AB = C, then what is A² equal to?