The following matrix $A$ is the transformation matrix of a linear operator A. Find the linear transformation matrix $B$ that represents the linear operator A relative to the basis $[1, 1, 0]^T$, $[0, 1, 1]^T$ and $[1, 2, 2]^T$.

'b' is obtained by summing up all the elements in $B$, taking the absolute value and then rounding to the nearest integer. What is the value of mod(b,5), where mod(.) is the modulo operator?