Question

Can you think of any 2x2 matrices d for which cd = dc for all 2x2 matrices c? give 2 different examples of such matricesd.

Answer 1

For any arbitrary 2x2 matrices $\mathbf C$ and $\mathbf D$, only one choice of $\mathbf D$ exists to satisfy $\mathbf{CD}=\mathbf{DC}$, which is the identity matrix.

There is no other matrix that would work unless we place some more restrictions on $\mathbf C$. One such restriction would be to ensure that $\mathbf C$ is not singular, or its determinant is non-zero. Then this matrix has an inverse, and taking $\mathbf D=\mathbf C^{-1}$ we'd get equality.