The product $$\left[ P \right]\,\,{\left[ Q \right]^T}$$ of the following two matrices $$\left[ P \right]\,$$ and $$\left[ Q \right]\,$$
where $$\left[ P \right]\,\, = \left[ {\matrix{ 2 & 3 \cr 4 & 5 \cr } } \right],\,\,\left[ Q \right] = \left[ {\matrix{ 4 & 8 \cr 9 & 2 \cr } } \right]$$ is

The determinant of the following matrix $$\left[ {\matrix{ 5 & 3 & 2 \cr 1 & 2 & 6 \cr 3 & 5 & {10} \cr } } \right]$$

Consider the following two statements.

$$(I)$$ The maximum number of linearly independent column vectors of a matrix $$A$$ is called the rank of $$A.$$

$$(II)$$ If $$A$$ is $$nxn$$ square matrix then it will be non-singular if rank of $$A=n$$

If $$A,B,C$$ are square matrices of the same order then $${\left( {ABC} \right)^{ - 1}}$$ is equal be