m : Type ?u.2654416
n : Type ?u.2654419
inst✝⁴ : DecidableEq n
inst✝³ : Fintype n
inst✝² : DecidableEq m
inst✝¹ : Fintype m
R : Type v
inst✝ : CommRing R
A : Matrix (Fin 3) (Fin 3) R
⊢ A 0 0 * (A 1 1 * A 2 2 + -(A 1 2 * A 2 1)) +
      (-(A 0 1 * (A 1 0 * A 2 2 + -(A 1 2 * A 2 0))) + (-1) ^ (1 + 1) * A 0 2 * (A 1 0 * A 2 1 + -(A 1 1 * A 2 0))) =
    A 0 0 * A 1 1 * A 2 2 - A 0 0 * A 1 2 * A 2 1 - A 0 1 * A 1 0 * A 2 2 + A 0 1 * A 1 2 * A 2 0 +
        A 0 2 * A 1 0 * A 2 1 -
      A 0 2 * A 1 1 * A 2 0
m : Type ?u.2654416
n : Type ?u.2654419
inst✝⁴ : DecidableEq n
inst✝³ : Fintype n
inst✝² : DecidableEq m
inst✝¹ : Fintype m
R : Type v
inst✝ : CommRing R
A : Matrix (Fin 3) (Fin 3) R
⊢ det A =
    A 0 0 * A 1 1 * A 2 2 - A 0 0 * A 1 2 * A 2 1 - A 0 1 * A 1 0 * A 2 2 + A 0 1 * A 1 2 * A 2 0 +
        A 0 2 * A 1 0 * A 2 1 -
      A 0 2 * A 1 1 * A 2 0
simp [Matrix.det_succ_row_zero, Fin.sum_univ_succ]
no goals
m : Type ?u.2654416
n : Type ?u.2654419
inst✝⁴ : DecidableEq n
inst✝³ : Fintype n
inst✝² : DecidableEq m
inst✝¹ : Fintype m
R : Type v
inst✝ : CommRing R
A : Matrix (Fin 3) (Fin 3) R
⊢ A 0 0 * (A 1 1 * A 2 2 + -(A 1 2 * A 2 1)) +
      (-(A 0 1 * (A 1 0 * A 2 2 + -(A 1 2 * A 2 0))) + (-1) ^ (1 + 1) * A 0 2 * (A 1 0 * A 2 1 + -(A 1 1 * A 2 0))) =
    A 0 0 * A 1 1 * A 2 2 - A 0 0 * A 1 2 * A 2 1 - A 0 1 * A 1 0 * A 2 2 + A 0 1 * A 1 2 * A 2 0 +
        A 0 2 * A 1 0 * A 2 1 -
      A 0 2 * A 1 1 * A 2 0
ring