var M = [ [1,2,3,4],
          [5,6,7,8],
          [9,1,2,3],
          [4,5,9,7] ];

function det(M) {
    if (M.length==2) { return (M[0][0]*M[1][1])-(M[0][1]*M[1][0]); }
    var answer = 0;
    for (var i=0; i< M.length; i++) {
        answer += Math.pow(-1,i)*M[0][i]*det(deleteRowAndColumn(M,i));
    }
    return answer;
}

function deleteRowAndColumn(M,index) {
    var temp = [];
    for (var i=0; i<M.length; i++) { temp.push(M[i].slice(0)); }
    temp.splice(0,1);
    for (var i=0; i<temp.length; i++) { temp[i].splice(index,1); }
    return temp;
}

document.getElementById('answer').innerHTML = det(M);