4 added 36 characters in body
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J, 8 bytes

1:e.#@C.

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Explanation

1:e.#@C.  Input: matrix M
      C.  FindConvert theeach cyclesrow offrom eacha rowpermutation to a list of cycles
    #@    LengthNumber of cycles in each cyclerow
1:        Constant function 1
  e.      Is 1 a member of the cycle lengths?

J, 8 bytes

1:e.#@C.

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Explanation

1:e.#@C.  Input: matrix M
      C.  Find the cycles of each row
    #@    Length of each cycle
1:        Constant function 1
  e.      Is 1 a member of the cycle lengths?

J, 8 bytes

1:e.#@C.

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Explanation

1:e.#@C.  Input: matrix M
      C.  Convert each row from a permutation to a list of cycles
    #@    Number of cycles in each row
1:        Constant function 1
  e.      Is 1 a member of the cycle lengths?
3 deleted 26 characters in body
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J, 8 bytes

1:e.#@C.

Try it online!Try it online!

Explanation

1:e.#@C.  Input: matrix M
      C.  Find the cycles of each row
    #@    Length of each cycle
1:        Constant function 1
  e.      Is 1 a member of the cycle lengths?

J, 8 bytes

1:e.#@C.

Try it online!

Explanation

1:e.#@C.  Input: matrix M
      C.  Find the cycles of each row
    #@    Length of each cycle
1:        Constant function 1
  e.      Is 1 a member of the cycle lengths?

J, 8 bytes

1:e.#@C.

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Explanation

1:e.#@C.  Input: matrix M
      C.  Find the cycles of each row
    #@    Length of each cycle
1:        Constant function 1
  e.      Is 1 a member of the cycle lengths?
2 added 216 characters in body
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J, 8 bytes

1:e.#@C.

Try it online!

Explanation

1:e.#@C.  Input: matrix M
      C.  Find the cycles of each row
    #@    Length of each cycle
1:        Constant function 1
  e.      Is 1 a member of the cycle lengths?

J, 8 bytes

1:e.#@C.

Try it online!

J, 8 bytes

1:e.#@C.

Try it online!

Explanation

1:e.#@C.  Input: matrix M
      C.  Find the cycles of each row
    #@    Length of each cycle
1:        Constant function 1
  e.      Is 1 a member of the cycle lengths?
1
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