Rabbits Seven

$b^1 = T_1^1 a^1 + T_2^1 a^2 + T_3^1 a^3$

$b^2 = T_1^2 a^1 + T_2^2 a^2 + T_3^2 a^3$

$b^3 = T_1^3 a^1 + T_2^3 a^2 + T_3^3 a^3$

If $T_j^i = \delta_j^i$ (where latex] \delta_j^i[/latex] is the Kronecker Delta) then

$T_1^1 =T_2^2 =T_3^3 = 1$

and we have the following:

$b^1 = T_1^1 a^1 = (1) a^1 = a^1$

$b^2 = T_2^2 a^2 = (1) a^2 = a^2$

$b^3 = T_3^3 a^3 = (1) a^3 = a^3$

We can write the following, because we were given that $T_j^i = \delta_j^i$ :

$T_j^i a^i = b^i$

$\delta_j^i a^i = b^i$