The smallest and largest Eigen values of the
following matrix are : $$\left[ {\matrix{ 3 & { - 2} & 2 \cr 4 & { - 4} & 6 \cr 2 & { - 3} & 5 \cr } } \right]$$

The two Eigen Values of the matrix $$\left[ {\matrix{ 2 & 1 \cr 1 & p \cr } } \right]$$ have a ratio of $$3:1$$ for $$p=2.$$ What is another value of $$'p'$$ for which the Eigen values have the same ratio of $$3:1$$?

What is the minimum number of multiplications involved in computing the matrix product $$PQR?$$ Matrix $$P$$ has $$4$$ rows and $$2$$ columns, matrix $$Q$$ has $$2$$ rows and $$4$$ columns and matrix $$R$$ has $$4$$ rows and $$1$$ column ______.

The inverse of the matrix $$\left[ {\matrix{ {3 + 2i} & i \cr { - i} & {3 - 2i} \cr } } \right]$$ is