Which of the following sets are a subspace of the set of all

Which of the following sets are a subspace of the set of all 3x3 matrices, explain.

a) W = A R3x3 { at least one entry of A is zero }

b)  = A R3x3 { AB = BA}, where B = [2 1 3; 2 3 1; 1 1 1]

Solution

a) Let W be the set of all 3 × 3 matrices

         here A gives it\'s R3x3

   so that we say

     W = A R3x3 { at least one entry of A is zero }

   what ever values we take in A.

b) here

    Let AB = BA

   where B = [2 1 3; 2 3 1; 1 1 1]

       and take A=[1 2 3; 5 4 3; 2 0 8]

and multiply it we different results,

some sets may be satisfy it.