Q.If $A$ is a square matrix such that $|A|\neq0$, then $A$ is called:

Whether a square matrix has an inverse depends entirely on whether its determinant is zero or not.

Testing each option against the definitions

1. A singular matrix is defined by $|A|=0$ — the opposite of what is given here, so (a) is wrong.
2. A non-singular matrix is defined by $|A|\neq0$ — exactly the condition given in the question. This is the correct answer.
3. A null (zero) matrix has every element equal to $0$ — a much stronger, unrelated condition; a null matrix is always singular ($|A|=0$ for it), so it cannot be the answer here.
4. A scalar matrix is a diagonal matrix with all equal diagonal entries — a statement about the PATTERN of entries, not about whether the determinant is zero; a scalar matrix can be either singular (if its diagonal value is $0$) or non-singular (any other value), so "scalar" is not implied by $|A|\neq0$ alone. …

Confusing 'singular' and 'non-singular' — remembering that singular sounds like it should mean 'special' or 'has an inverse', when it is act …