The image contains a set of mathematical problems related to matrices and determinants. Here's an outline of the tasks presented:

Tasks Overview:

1. Matrix Equation: Solve for $X$ in the matrix equation $AX - C = BX$.

2. Input-Output Model: Given matrix $A$ and vector $Y$, find vector $X$ satisfying $AX + Y = X$.

3. Production Pricing Model: Using matrix $A$ and vector $v$, find the price vector $p$ that satisfies $p = A^T p + v$.

4. Linear System: Determine the number of solutions for a system of linear equations, without explicitly solving it.

5. Matrix Commutation: Identify all matrices $B$ (excluding the null and identity matrices) for which $AB = BA$, where $A$ is given.

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