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STD 12 - 3 and 4 . determinant and metrices — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 3 and 4 . determinant and metrices4 Marks
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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