Step 1: Recall what borax is.
Borax is sodium tetraborate, $Na_2B_4O_7 \cdot 10H_2O$. When it dissolves in water it undergoes hydrolysis.
Step 2: Write the hydrolysis.
\[ Na_2B_4O_7 + 7H_2O \rightarrow 2NaOH + 4H_3BO_3 \] So the two products are sodium hydroxide and boric acid.
Step 3: Classify product A.
$NaOH$ is fully ionised in water, so it is a strong base.
Step 4: Classify product B.
$H_3BO_3$ (boric acid) only weakly accepts $OH^-$ from water, so it is a weak acid.
Step 5: Net effect.
Because a strong base and a weak acid form, a borax solution is basic, which is why borax is used as a buffer and cleaning aid.
Step 6: Conclusion.
So A is a strong base and B is a weak acid. \[ \boxed{\text{Strong base, Weak acid}} \]