Suppose A is an n n invertible matrix Can it have a zero ei

Suppose A is an n × n invertible matrix. Can it have a zero eigenvalue? Justify your answer.

Thank you in advance !

Solution

Given that A is a square matrix

nxn

which is invertible.

Hence det A is not zero.

This means A-0I not equal to 0

Hence 0 cannot be an eigen value for .A

Note: Only singular square matrices can have 0 as eigen value.