If the matrices `A=[(1,2),(3,4)] and B=[(a,b),(c,d)] (a,b,cd` not all simultaneously zero) commute, find the value of `(d-b)/(a+c-b).` Also show that the matrix which commutes with A is of the form `[(alpha-beta,(2beta)/3),(beta,alpha)]`

Explanation

To solve the problem step by step, we need to find the value of \((d-b)/(a+c-b)\) given that matrices \(A\) and \(B\) commute, and also show that the matrix which commutes with \(A\) is of the form \(\begin{pmatrix} \alpha - \beta & \frac{2\beta}{3} \\ \beta & \alpha \end{pmatrix}\).

### Step 1: Define the matrices
We have:
\[ A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}, \quad B = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \]

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