‘0' is a characteristic root of a matrix, if and only if, the matrix is

Singular Matrix:  A matrix is said to be singular if and only if its determinant is equal to zero.

Singular matrix example:

A = \(\begin{bmatrix} 1 & 2\\ 1 & 2 \end{bmatrix}\)

Singular Matrix Properties:

• A matrix is said to be singular if and only if its determinant is equal to zero.
• A singular matrix is a matrix that has no inverse such that it has no multiplicative inverse.
   

Application:

Characteristics equation of matrix can be written as,

|A - λI| = 0

If; λ = 0

|A| = 0

Hence, the matrix is singular matrix.