If A and B are square matrices of same order satisfying A - B - AB- thenA- A - B - BAB- A - B - BAC- AB - BAD- AB - BA

The correct option is C AB=BAGiven, A+B=AB ⋯ (1) nbsp; ⇒ AB A B+I=I ⇒ (I A) (I B)=I ⇒ I A and I B are inverse of each other. So, (I B) (I A)=I ⇒ I A B+BA ...

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Byju's Answer

Standard XII

Mathematics

Inverse of a Matrix

If A and B ar...

Question

If $A$ and $B$ are square matrices of same order satisfying $A + B = A B,$ then

A B = B A

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A B = - B A

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A + B = - B A

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A - B = B A

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Solution

The correct option is A $A B = B A$
Given, $A + B = A B \dots (1)$
$\Rightarrow A B - A - B + I = I$
$\Rightarrow (I - A) (I - B) = I$
$\Rightarrow I - A$ and $I - B$ are inverse of each other.
So, $(I - B) (I - A) = I$
$\Rightarrow I - A - B + B A = I$
$\Rightarrow A + B = B A \dots (2)$

From $(1)$ and $(2),$
$A B = B A$

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If A and B are square matrices of same order satisfying A+B=AB, then

The correct option is A AB=BAGiven, A+B=AB ⋯(1) ⇒AB−A−B+I=I ⇒(I−A)(I−B)=I ⇒I−A and I−B are inverse of each other. So, (I−B)(I−A)=I ⇒I−A−B+BA=I ⇒A+B=BA ⋯(2) From (1) and (2), AB=BA

If $A$ and $B$ are square matrices of same order satisfying $A + B = A B,$ then