Matrices A and B will be inverse of each other only if - Vidyadip

MCQ

Matrices $\mathrm{A}$ and $\mathrm{B}$ will be inverse of each other only if

✓
$A B=B A=I$
B
$A B=0,\, B A=I$
C
$A B=B A=0$
D
$A B=B A$

✓

Answer

Correct option: A.

$A B=B A=I$

a
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 $A B=B A=I$.

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