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Question

If $$A$$ and $$B$$ are two matrices such that $$AB = A$$ and $$BA = B$$, then $$B^{2}$$ is equal to


A
B
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B
A
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C
1
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D
0
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Solution

The correct option is A $$B$$
Given for $$A$$ and $$B$$ are two matrices such that $$AB = A$$.....(1) and $$BA = B$$......(2).

Now, from (2) we have,

$$B^2=(BA)(BA)$$

$$\Rightarrow B^2=B(AB)A$$ [ Since matrix multiplication is associative]

$$\Rightarrow B^2=B(A)A$$ [ Using (1)]

$$\Rightarrow B^2=(BA)A$$ [ Since matrix multiplication is associative]

$$\therefore  B^2=BA=B$$ [ Using (2)]

Mathematics

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