Question 1058626
The matrix B^2 is:


     *[illustration Matrices.png]


To make B^2 = I3, the following must be true:


2b21 = 0 --> b21 = 0


2b32 = 0 --> b32 = 0


2b31 + b21b32 = 0 --> 2b31 + 0*0 = 0 --> b31 = 0


Thus, b21, b31, and b32 must all be 0.


Edit in response to follow-up comment from OP:


If b22 = -1 instead of b22 = 1 as originally posted, then B^2 would be:


 *[illustration Matrices2.png]


In this case, b21 and b32 could be any value to make B^2 = I3. In addition,
b31 = -(b21 * b32)/2.