ISI2017-DCG-4

Question

If $A$ is a $3 \times 3$ matrix satisfying $A^3 – A^2 +A-I= O$ (where $O$ is the zero matrix and $I$ is the identity matrix) then the value of $A^4$ is

• A. $A$
• B. $O$
• C. $I$
• D. none of these

Answer 1

since A^3 -A^2 +A+I =0

then A^3 -A^2 +A= I

=> A(A^2 -A + I)= I

=> A=I

so A^4= I^4=I

=> A^4= I