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

If $$A = \left[ {\matrix{ 1 & { - 1} \cr { - 1} & 1 \cr } } \right]$$, then the expression A³ $$-$$ 2A² is

If $$A = \left( {\matrix{ 1 & 2 \cr 2 & 3 \cr 3 & 4 \cr } } \right)$$ and $$B = \left( {\matrix{ 1 & 2 \cr 2 & 1 \cr } } \right)$$, then which one of the following is correct?