The value of $k$, for which the pair of linear equations $kx + y = k^2$ and $x + ky = 1$ have infinitely many solutions is

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Step 1: For infinitely many solutions: $\frac{k}{1} = \frac{1}{k} = \frac{k^2}{1}$. From $\frac{k}{1} = \frac{1}{k} \Rightarrow k^2 = 1 \Rightarrow k = \pm 1$. Check: $k = 1$ gives $\frac{1}{1} = \frac{1}{1} = \frac{1}{1}$ ✓. $k = -1$ gives $\frac{-1}{1} = \frac{1}{-1} = \frac{1}{1}$ ✗. So $k = 1$

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