A , B are 2x2 matrices in which
det A=det B=tr(A)=tr(B)=7
tr- is trace ,the sum of the diagonal
could we link A and B
by
B=P-1AP
yes, if A is invertible, and B is invertible, then AB is invertible.
why? since we can form the matrices $\displaystyle A^{-1}$ and $\displaystyle B^{-1}$, the product $\displaystyle B^{-1}A^{-1}$ exists.
but $\displaystyle (AB)(B^{-1}A^{-1}) = A(BB^{-1})A^{-1} =AIA^{-1} = AA^{-1} = I$,
and $\displaystyle (B^{-1}A^{-1})(AB) = B^{-1}(A^{-1}A)B = B^{-1}IB = B^{-1}B = I$.