Question

Let P be a non-singular matrix and
I + P + p2 + ....... + P = 0 then p-1 is​

Answer 1

Answer:

We have I+p+p

2

+.....+p

n

=O ----------(1)

Since p is a nonsingular matrix, p is invertible.

Multiplying both sides of (1) by p

−1

, we get

p

−1

+I+Ip+.....+p

n−1

I=O.p

−1

or p

−1

+I(1+p+......+p

n−1

)=O

or p

−1

=−I(I+p+p

2

+.....+p

n−1

)=−I(−p

n

)=p

n

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