Question

Determinant of Nilpotent matrix is 0​

Answer 1

Answer:

The determinant and trace of a nilpotent matrix are always zero. The only nilpotent diagonalizable matrix is the zero matrix. Every singular matrix can be expressed as a product of nilpotent matrices.

Answer 2

Answer:

A square matrix A in which there exist a number n such that

A

n

=

0

then the matrix A is called the Nilpotent matrix and the smallest number n such that

A

n

=

0

is called the index of the matrix.