Represent the matrix as a bitmask where each bit corresponds to a cell (0 for 0, 1 for 1). For an `m x n` matrix, the bitmask will be an integer in the range `[0, 2^(m*n) - 1]`.

Use BFS to explore all possible states (bitmasks) starting from the initial state. For each state, generate all possible next states by flipping each cell (and its adjacent cells) and check if the new state has been visited before. If the new state is all zeros, return the number of operations taken to reach it.

To optimize, note that flipping a cell twice is equivalent to not flipping it at all. Thus, for each cell, you only need to consider flipping it once or not at all. This reduces the branching factor from `m*n` to `m*n` (since each cell can be flipped or not), but the BFS will still explore all possible combinations.