Matrix Game

Two players play a game on an n x m binary matrix (each cell is 0 or 1). In each turn, a player selects a cell (i, j) that contains a 1, then sets all cells in row i and column j to 0. The player who makes the last move (removes the last available 1) wins. Both play optimally. Determine whether the first player has a winning strategy. If the matrix contains no 1s, the first player cannot move and loses immediately.

Examples
Input: [[1]]
Output: true
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Matrix Game

Two players play a game on an n x m binary matrix (each cell is 0 or 1). In each turn, a player selects a cell (i, j) that contains a 1, then sets **all** cells in row i and column j to 0. The player who makes the last move (removes the last available 1) wins. Both play optimally. Determine whether the first player has a winning strategy. If the matrix contains no 1s, the first player cannot move and loses immediately.