m = {{1, -1},{0.5, 0.5}};m//MatrixForm

stretch ={{l,0},{0,1}};stretch//MatrixForm

shear = {{1,k},{0,1}} ; shear//MatrixForm

squeeze = {{s,0},{0,1/s}}; squeeze // MatrixForm

rot = {{Cos[θ],-Sin[θ]},{Sin[θ],Cos[ θ]}}; rot // MatrixForm

$Assumptions={{l,k,s}∈Reals}

Solve[squeeze.rot.{{1,0},{0,1}}== m,{θ,s},Reals]