Question

If the determinant value of any square matrix is zero then
it is called -
a) Scalar matrix
b) Diagonal matrix
c) Singular matrix
d) Triangular matrix​

Answer 1

If the determinant of a square matrix n×n A is zero, then A is not invertible. This is a crucial test that helps determine whether a square matrix is invertible, i.e., if the matrix has an inverse. When it does have an inverse, it allows us to find a unique solution, e.g., to the equation Ax=b given some vector b.

Answer 2

Answer:

C

Step-by-step explanation:

There are two terms in common use for a square matrix whose determinant is zero: “noninvertible” and “singular”.

There’s a theorem in linear algebra that says a square matrix has an inverse if and only if its determinant is not zero.  

Thus, the matrix is noninvertible if and only if its determinant is zero.

The other term for a matrix that’s not invertible is “singular matrix”. As to why it’s called that, see the question Why is a matrix whose determinant is 0 called a singular matrix?  

When teaching a course in linear algebra, I use whichever term the textbook uses, but I mention the other term because both are used.