Non-singularity of a square matrix The diagonal elements of a square matrix $M$ are odd integers while the off diagonals are even integers. Then can we say that $M$ must be non-singular?
We can easily comment on the singularity of the matrix $M$. Let us take the identity matrix of order $2$ which is non-singular.So can I say the $M$ must be non-singular for every such case?
please help me to clear this idea.

Yes, this is true. Consider the matrix $A$ and its determinant modulo $2$. Then $A$ is congruent to $I_n$ modulo $2$, whose determinant is $1$. Hence $A$ has nonzero determinant, and so is non-singular.
