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?

Consider the set A of all matrices of order 3 $$\times$$ 3 with entries 0 or 1 only. Let B be the subset of A consisting of all matrices whose determinant is 1. Let C be the subset of A consisting of all matrices whose determinant is $$-$$1. Then which one of the following is correct?