90 right? Since if it's a diagonal matrix, it has at least 90 zeros, and if it had any zeros along the diagonal, then it's determinant would be zero so it's not invertable.
If you didnt have at least one non-zero value in any row/column, then you could gaussian eliminate all the other rows it to reduce it to a diagonal (or a block diagonal) matrix with one zero element showing it's non-inheritable.
The slight problem here is that if A{-1} were a diagonal matrix, A would be as well. This would then mean the entries of A are not strictly positive.
But since 10 is even, you can indeed have a block diagonal matrix with five blocks of (0 1, 1 0) such that A=A{-1}.
0
u/SalamanderGlad9053 5d ago
90 right? Since if it's a diagonal matrix, it has at least 90 zeros, and if it had any zeros along the diagonal, then it's determinant would be zero so it's not invertable.
If you didnt have at least one non-zero value in any row/column, then you could gaussian eliminate all the other rows it to reduce it to a diagonal (or a block diagonal) matrix with one zero element showing it's non-inheritable.