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Checking that a matrix space is invariant with respect to a linear map

I am trying to solve Checkpoint 1.4.4 from "A Second Course in Linear Algebra" from Robert A. Beezer. I need to prove that V is invariant with respect to B.

But I think it is not actually true. In order to prove it, I am comparing the rank(V) = 3 and the rank of (V | BV) which is 4. So there must be a vector in BV that is linearly independent with the vectors of V. Do I miss something?

Here is my code:

B = matrix (
            [[4 , 47 , 3 , -46 , 20] ,
            [10 , 61 , 8 , -56 , 10] ,
            [ -10 , -69 , -7 , 67 , -20] ,
            [11 , 70 , 9 , -64 , 12] ,
            [3 , 19 , 3 , -16 , 1]])

 V = matrix([[1, 3, -2],
                    [1, 3, 3], 
                    [-1, -2, 2],
                    [1, 4, 3],
                    [0, 2, 1]])

 V.augment(B*V.rank() == V.rank()

Checking that a matrix space is invariant with respect to a linear map

I am trying to solve Checkpoint 1.4.4 from "A Second Course in Linear Algebra" from Robert A. Beezer. I need to prove that V is invariant with respect to B.

Here is my code:

B = matrix (
            [[4 , 47 , 3 , -46 , 20] ,
            [10 , 61 , 8 , -56 , 10] ,
            [ -10 , -69 , -7 , 67 , -20] ,
            [11 , 70 , 9 , -64 , 12] ,
            [3 , 19 , 3 , -16 , 1]])

 V = matrix([[1, 3, -2],
                    [1, 3, 3], 
                    [-1, -2, 2],
                    [1, 4, 3],
                    [0, 2, 1]])

 V.augment(B*V.rank() V.augment(B*V).rank() == V.rank()