For x>0, let A=⎡⎢
⎢
⎢⎣x+1x000x00016⎤⎥
⎥
⎥⎦ and B=⎡⎢
⎢
⎢
⎢
⎢
⎢
⎢⎣5xx2+10003x00014⎤⎥
⎥
⎥
⎥
⎥
⎥
⎥⎦ be two matrices.
Two other matrices X and Y are defined as
X=(AB)−1+(AB)−2+AB−3+⋯(AB)−n and Y=limn→∞X. If tr(P) denotes the trace of matrix P, then the least positive integral value of tr(AY) is