Question

The matrix P is the inverse of a matrix Q. If i denotes the identity matrix, which one of the following options is correct?

• A. PQ = 1 but QP $\ne$ 1
• B. QP = 1 but PQ $\ne$ 1
• C. PQ = 1 and QP $=$ 1
• D. PQ - QP =1

Answer 1

The correct option is C PQ = 1 and QP $=$ 1

Given, $P=Q^{-1}$
Post multiply by Q
$PQ=Q^{-1}Q$ (we know $Q^{-1}Q=1$)
$PQ=1$
Again premultiply by Q
$QP=Q{Q}^{-1}$
$QP=1\left(Q{Q}^{-1=1}\right)$
So,$PQ=I$ and $QP=I$