Consider the following in respect of non-singular matrices A and B:

I. $(AB) ^ {- 1} = A ^ {- 1} B ^ {- 1}$

II. $ (BA)(AB)^{-1}=I$ = I where I is the identity matrix

III. $ (AB)^{T}=A^{T}B^{T} $

How many of the above are correct?

Let 1, ω, $\omega ^ 2$ be three cube roots of unity. If x = a + b $y=a\omega +b\omega ^{2}, z=a\omega ^{2}+b\omega$ then what is $ x ^ 2 + y ^ 2 + z ^ 2$ equal to?

How many 4-digit numbers that are divisible by 4 can be formed using the digits 1, 2, 3 and 4 (repetition of digits is not allowed)?