Compute AB and BA, whichever exists when
(i) `A=[{:(2,-1),(3," "0),(-1," "4):}]" and "B=[{:(-2,3),(0,4):}]`
(ii) `A=[{:(-1,1),(-2,2),(-3,3):}]" and "B=[{:(" "3,-2," "1),(" "0," "1," "2),(-3," "4,-5):}]`
(iii) `A=[{:(0,1,-5),(2,4," "0):}]" and "B=[{:(1,3),(-1,0),(0,5):}]`
(iv) `A=[1" "2" "3" "4]" and "B=[{:(1),(2),(3),(4):}]`
(v) `A=[{:(2,1),(3,2),(-1,1):}]" and "B=[{:(1,0,1),(-1,2,1):}]`

Explanation

To compute the products \(AB\) and \(BA\) for the given matrices, we will follow the steps outlined below for each part of the question.

### (i) Given:
\[ A = \begin{pmatrix} 2 & -1 \\ 3 & 0 \\ -1 & 4 \end{pmatrix}, \quad B = \begin{pmatrix} -2 & 3 \\ 0 & 4 \end{pmatrix} \]

**Step 1: Determine the dimensions of matrices A and B.**
- Matrix \(A\) is \(3 \times 2\) (3 rows and 2 columns).
- Matrix \(B\) is \(2 \times 2\) (2 rows and 2 columns).
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