= Solution
The <orthonormal> columns satisfy $\|a\|_2=\|b\|_2=1$ and $a^Tb=0$. By part (i), $Q_1a=e_1$. A product of <orthogonal matrices> is an <orthogonal matrix>, since $Q_1^TQ_1=I$. Consequently
$$
0=a^Tb=(Q_1a)^T(Q_1b)=e_1^TQ_1b.
$$
The last expression is the first coordinate of the transformed second column. Thus \b[the first row is]
$$
\boxed{(Q_1A)_{1,:}=(1,0).}
$$
The one in the first entry uses the nonnegative retained-coordinate convention. A different consistent sign convention could give $(-1,0)$ instead; the second entry must still be zero by preservation of the <inner product>.
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