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

If $$A$$ is any $$nxn$$ matrix and $$k$$ is a scalar then $$\left| {kA} \right| = \alpha \left| A \right|$$ where $$\alpha $$ is

The number of terms in the expansion of general determinant of order $$n$$ is