Problem
COM-B1-M06-P016 One Minus After Row Flips
#16
★★★☆☆ Level 3 of 5
In a \(4\) by \(4\) table, all signs are \(+\). In one move, one may change all signs in a row or a column. Can a table with exactly one minus be obtained?
Four signs change, so the product of all signs is preserved.
Each move changes \(4\) signs, so the product of all \(16\) signs is multiplied by \((-1)^4=1\). Initially the product is \(+1\). With exactly one minus, it is \(-1\). Impossible.
Table version of sign product.