Let L = [ [2, 3], [1, 4] ] and R = [ [3, 0], [1, 2] ]. We need A such that L A = R. Since L is invertible (det L = 24 31 = 5 0), multiply both sides on the left by L^{-1}: A = L^{-1} R. Compute L^{-1}: L^{-1} = (1/5) [ [4, 3], [1, 2] ]. Now multiply: [ [4, 3], [1, 2] ] [ [3, 0], [1, 2] ] = [ [43 + (3)1, 40 + (3)2], [ (1)3 + 21, (1)0 + 22 ] ] = [ [9, 6], [1, 4] ]. Therefore, A = (1/5) [ [9, 6], [1, 4] ] = [ [9/5, 6/5], [1/5, 4/5] ]. Check: [ [2,3],[1,4] ] [ [9/5, 6/5], [1/5, 4/5] ] = [ [3,0],[1,2] ]