Wolfram Language (Mathematica), 25 bytes

#||#/.{a_..}:>Tr@a==1&

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Returns True if the matrix has a single line, and nonTrue otherwise.

Wolfram Language (Mathematica), 25 bytes

#||#/.{a_..}:>Tr@a==1&

Try it online!

Returns True if the matrix has a single line, and nonTrue otherwise.

#||# input OR its tranpose
 /.{a_..}:> replace lists of repeated elements with
 Tr@a==1 (is the sum of that element equal to 1?)

Then, any Or expression with True as an argument gets reduced to True.