Chapter 3 Matrices EXERCISE 3.4
EXERCISE 3.4
1. Matrices $A$ and $B$ will be inverse of each other only if
(A) $AB=BA$ (B) $AB=BA=0$
(C) $AB=0, BA=I$ (D) $AB=BA=I$
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Solution
We know that if $A$ is a square matrix of order $m$, and if there exists another square matrix $B$ of the same order $m$, such that $A B=B A=I$, then $B$ is said to be the inverse of $A$. In this case, it is clear that $A$ is the inverse of $B$.
Thus, matrices $A$ and $B$ will be inverses of each other only if $A B=B A=I$.
