Question

Найти все матрицы комутативные данной
А 1 1
-1 -1

Answer 1

A = 1 1  
      -1 -1
B = b11 b12
       b21 b22
AB = BA
AB= b11+b21 b12+b22
        -b11-b12 -b21-b12
BA = b11-b12 b11-b12
         b21-b22 b21-b22
=> b11+ b21 = b11 - b12 => b21 = -b12
     b12 + b22 = b11 - b12 => 2b12 = b11 - b22 => b11 = b22 = b
     -b11 - b12 = b21 - b22 => 3b12 = -b21 => b12 = 0
     -b21 - b22 = b21 - b22 => b21 = 0
=> B = b 0 
            0 b
для всех b из R