JavaScript (ES6), 62 bytes
Returns false for Hadamard or true for non-Hadamard.
m=>m.some((p,i)=>m.some(q=>i--*p.reduce((t,v,x)=>t+v*q[x],0)))
Arnauld
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m=>m.some((p,i)=>m.some(q=>i--*p.reduce((t,v,x)=>t+v*q[x],0)))