If A and B are 3 3matrices such that AB = A and BA = B, then - Vidyadip

MCQ

If $A$ and $B$ are $3 \times 3$matrices such that $AB = A$ and $BA = B$, then

A
${A^2} = A$ and ${B^2} \ne B$
B
${A^2} \ne A$ and ${B^2} = B$
✓
${A^2} = A$ and ${B^2} = B$
D
${A^2} \ne A$ and ${B^2} \ne B$

✓

Answer

Correct option: C.

${A^2} = A$ and ${B^2} = B$

c
Given that$AB = A$,$B = I$ $⇒$ $BA = B,$

$\therefore A = I$

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