If A + A + A = B A then B A is ?
Answers
Step-by-step explanation:
A +A + A = BA
3A = BA;
SOLVE FOR B
B = 3A/A
B = 3;
SUBSTITUTE VALUE FOR B IN EQUATION
AND SOLVE FOR A
3A = 3A, A = 1
ANSWER B = 3,
A = 1
CHECK
3(1) = 3(1)
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Question
If AB=A and BA=B, then which of the following is/are true?
This question has multiple correct options
A
A is idempotent
B
B is idempotent
C
AT is idempotent
D
none of these
Medium
Solution
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Correct option is
A
A is idempotent
B
B is idempotent
C
AT is idempotent
Given, AB=A and BA=B
Take, AB=A
⇒A(BA)=A [ Since, B=BA ]
⇒(AB)A=A
⇒AA=A [ Since, AB=A ]
⇒A2=A
Therefore, A is an idempotent matrix.
Take, BA=B
⇒B(AB)=B [ Since, A=AB ]
⇒(BA)B=B
⇒BB=B [ Since, BA=B ]
⇒B2=B
Therefore, B is an idempotent matrix.
Now, A=AB
Applying transpose on both sides, we get
AT=(AB)T
⇒AT=BT.AT....(i)
Also, B=BA
Applying transpose on both sides, we get
B