The Characteristic Polynomial of a 5 × 5 Matrix Is $\lambda ^ { 5 } - 24 \lambda ^ { 4 } + 189 \lambda ^ { 3 } - 486 \lambda ^ { 2 }$

Multiple Choice

The characteristic polynomial of a 5 × 5 matrix is given below. Find the eigenvalues and their multiplicities.
- $\lambda ^ { 5 } - 24 \lambda ^ { 4 } + 189 \lambda ^ { 3 } - 486 \lambda ^ { 2 }$

A) 0 (multiplicity 2) , 9 (multiplicity 2) , 6 (multiplicity 1 )
B) 0 (multiplicity 2) , $- 9$ (multiplicity 2) , -6 (multiplicity 1)
C) 0 (multiplicity 2) , $- 9$ (multiplicity 2) , 6 (multiplicity 1 )
D) 0 (multiplicity 1) , 9 (multiplicity $3 ) , 6$ (multiplicity 1 )