GATE Papers >> Civil >> 2017 >> Question No 1

Question No. 1 Civil | GATE 2017

The matrix P is the inverse of a matrix Q. If I denotes the identitiy matrix, which one of the following option is correct?


Answer : (C) $ \mathrm{PQ}\;=\mathrm I $ and $ \mathrm{QP}\;=\;\mathrm I $


Solution of Question No 1 of GATE 2017 Civil Paper

Given, P = Q-1

Post multiply by Q

PQ = Q-1Q (we know Q-1Q = I)

PQ = I

Again premultiply by Q

QP = QQ-1

QP = I (QQ-1 = I)

So, PQ = I and QP = I

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