What does it mean for a matrix to be singular?a.It is equal to its inverse.b.It is equal to its transpose.c.It is a square matrix.d.It has no inverse

To understand what it means for a matrix to be singular, let's analyze each of the provided options:

1. Option a: It is equal to its inverse.
   This is not correct. A singular matrix does not have an inverse, so it cannot be equal to its inverse.

2. Option b: It is equal to its transpose.
   A matrix being equal to its transpose describes a symmetric matrix, which is not necessarily related to the singularity of the matrix.

3. Option c: It is a square matrix.
   While singular matrices must be square (they are defined only in that context), mere squareness does not imply singularity, as not all square matrices are singular.

4. Option d: It has no inverse.
   This is the correct option. A singular matrix is defined as a square matrix that does not have an inverse, typically because its determinant is zero.

Final Answer

The correct answer is d. It has no inverse.