Školjka

%V0 Consider the two square matrices $$A=\begin{bmatrix}+1 &+1 &+1&+1 &+1\\+1 &+1 &+1&-1 &-1\\ +1 &-1&-1 &+1&+1\\ +1 &-1 &-1 &-1 &+1\\ +1 &+1&-1 &+1&-1\end{bmatrix}\quad\text{ and }\quad B=\begin{bmatrix}+1 &+1 &+1&+1 &+1\\+1 &+1 &+1&-1 &-1\\ +1 &+1&-1&+1&-1\\ +1 &-1&-1&+1&+1\\ +1 &-1&+1&-1 &+1\end{bmatrix}$$ with entries $+1$ and $-1$. The following operations will be called elementary: (1) Changing signs of all numbers in one row; (2) Changing signs of all numbers in one column; (3) Interchanging two rows (two rows exchange their positions); (4) Interchanging two columns. Prove that the matrix $B$ cannot be obtained from the matrix $A$ using these operations.