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# Matrices $A$ and $B$ will be inverse of each other only if

$\begin{array}{l l} (A) \; AB = BA & (B) \; AB = BA = 0 \\ (C) \; AB = 0, BA = I & (D) \; AB = BA = I \end{array}$

Toolbox:
• If we multiply a matrix with its inverse, the resulting matrix will be an identity matrix.
Step 1: Matrices A & B will be inverse of each other only if $AB=BA=I$
Hence (D) is the right option.

edited Mar 19, 2013