Is this Pascal's Matrix?
Brachylog, 28 24 23 bytes

This feels quite long but here it is anyway


-4 bytes thanks to DLosc by compressing the optional flips
-1 bytes thanks to DLosc again by doing the partial sums in 1 go


{|↔}\↰₁{k{a₀ᶠ+ᵐ}ᵐ⊆?h=₁}

Explanation

{|↔}\↰₁{k{a₀ᶠ+ᵐ}ᵐ⊆?h=₁}       # Tests if this is a pascal matrix:
{|↔}\↰₁                       #     By trying to get a rows of 1's on top
{|↔}                          #       Through optionally mirroring vertically
     \                        #       Transposing
      ↰₁                      #       Through optionally mirroring vertically

       {k{a₀ᶠ+ᵐ}ᵐ⊆?h=₁}       #     and checking the following
                  ?h=₁        #        first row is a rows of 1's
        k{     }ᵐ             #        and for each row except the last
          a₀ᶠ+ᵐ               #          calculate the partial sum by
          a₀ᶠ                 #             take all prefixes of the input
             +ᵐ               #             and sum each
               ⊆?             #        =&gt; as a list is a subsequence of the rotated input


Try it online!