Question

# A square matrix P satisfies P2=I−P, where I is an identity matrix of order as order of P. if Pn=5I−8P,then n=

A
4
B
5
C
6
D
7

Solution

## The correct option is A 6Since P2=I−P(Given)−(1) P3=P(I−P) P3=P−P2=P−(I−P) P3=2P−I Similarly P4=2P2−P=2I−3P AND P5=5P−3I P6=5P2−3P=5I−8P ∴n=6

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