Question: solve matrix equation

Hi guys,

I want to solve the matrix equation. suppose we have a matrix A 4*4 which only first array of it (1,1) is equal to n and another matrix such as S which is again 4*4 and generally, we don't know its arrays and we want A and S satisfy the following equation:

S*A*inverse(S)=A

how we can find out arrays of S?

A=Matrix([[1,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0]])

S=Matrix([[a,b,c,d],[e,f,g,h],[I,j,k,l],[m,n,o,p]])

 

thanks

 

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