Question

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$\LARGE\color{black}{\colorbox{#FF7968}{Q}\colorbox{#4FB3F6}{U}\colorbox{#FEDD8E}{E}\colorbox{#FBBE2E}{S}\colorbox{#60D399}{T}\colorbox{#6D83F3}{I}\colobox{#FF7968}{O}\colorbox{#4FB3F6}{N}}$

If A is any non zero matrix, such that A³=O , then find A² + A + I​

Answer 1

Step-by-step explanation:

since the eigenvalue of matrix A is zero

(I−A) is invertible we have

(I−A)(I+A+A

2

)=I−A

3

=I−0=I

(I−A)(I+A+A

2

)=I

∴I+A+A

2

=(I−A)

−1