Question

Which statement is true about the determinant of a matrix? The determinant of a singular matrix is equal to zero. The determinant of an inverse matrix is equal to zero. The determinant of an identity matrix is equal to zero. The determinant of a zero matrix is equal to one.

Answer 1

A determinant is a quantity that is obtained by the addition of products of the elements of a square matrix according to a given rule. The true statement about the determinants from the given choices is that:
The determinant of a singular matrix is equal to zero.

It's good to note that the determinant of an identity matrix is 1 NOT 0

Answer 2

The true statement about the Determinant of a determinant is "Determinant of a singular matrix is equal to zero".

What is the determinant of a matrix?

Determinants are considered as a scaling factor of matrices.

They can be considered as functions of stretching out and the shrinking in of the matrices.

Determinants take a square matrix as the input and return a single number as its output.

A square matrix can be defined as a matrix that has an equal number of rows and columns.

We know that, the square matrix whose Determinant is zero than these matrix refers to the singular matrix.

The Determinant of inverse matrix can never be zero.

The Determinant of an identity matrix is always 1.

The determinant of a zero matrix is always 0.

Hence from above properties of matrix the correct option is option (a). The determinant of a singular matrix is equal to zero.

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