If AB - A and BA - B- thenA- A2 B-A2B- B 2 A - B 2C- ABA - AD- BAB - B

The correct options are A A^2B = A^2 nbsp; B B^2A = B^2 C ABA = A nbsp; D BAB = BGiven, AB = A and BA = B We have, A^2B = A(AB) = AA = A^2 B^2A = B(BA) = ...

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Byju's Answer

Standard XII

Mathematics

Multiplication of Matrices

If AB = A and...

Question

If $A B = A$ and $B A = B$ , then

A^{2} B = A^{2}

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B^{2} A = B^{2}

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A B A = A

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B A B = B

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Solution

The correct options are
A $A^{2} B = A^{2}$

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

D $B A B = B$
Given, $A B = A$ and $B A = B$
We have, $A^{2} B = A (A B) = A A = A^{2}$ $B^{2} A = B (B A) = B B = B^{2}$ $A B A = A (B A) = A B = A$ and $B A B = B (A B) = B A = B .$

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If AB=A and BA=B, then

The correct options are A A2B=A2 B B2A=B2 C ABA=A D BAB=BGiven, AB=A and BA=B We have, A2B=A(AB)=AA=A2 B2A=B(BA)=BB=B2 ABA=A(BA)=AB=A and BAB=B(AB)=BA=B.

If $A B = A$ and $B A = B$ , then

The correct options are
A $A^{2} B = A^{2}$

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

D $B A B = B$
Given, $A B = A$ and $B A = B$
We have, $A^{2} B = A (A B) = A A = A^{2}$ $B^{2} A = B (B A) = B B = B^{2}$ $A B A = A (B A) = A B = A$ and $B A B = B (A B) = B A = B .$