Let n = B ;') and it 2 A 0 -5 -1 2 1 B 4 -2 B-3 0 3 5 . Then the product AB=
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Answer:
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Step-by-step explanation:
Correct option is B)
Given
A=[
1
3
2
4
]B=[
a
0
0
b
]
Finding AB
AB=[
1
3
2
4
][
a
0
0
b
]=[
a+2×0
3×a+4×0
1×0+2×b
3×0+4×b
]
AB=[
a
3a
2b
4b
]
Finding BA
BA=[
a
0
0
b
][
1
3
2
4
]=[
a+0×3
0×1+3b
2a+0×4
0×2+4b
]
BA=[
a
3b
2a
4b
]
If AB=BA
[
a
3a
2b
4b
]=[
a
3b
2a
4b
]
Comparing each element we get
a=a,2b=2a
⇒a=b
∴There are infinitely many b's
for which AB=BA
Answer=a
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