Consider the linear transformation: M12 P1 from the set of 1 2 matrices to the

Question:

Consider the linear transformation: M12 → P1 from the set of 1 × 2 matrices to the set of polynomials of degree at most 1, defined by
S ([a b]) = (3a + b) + (5a + 2b)x
Prove that S is invertible. Then show that the linear transformation
R: P1 → M12, R(r + sx) = [(2r - s) (-5r + 3s)]
is the inverse of S, that is S-1 = R.