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Question
If A and B are two matrices such that AB = A and BA = B, then B2 is equal to
Options
B
A
1
0
Solution
B
\[Here, \]
\[AB = A . . . \left( 1 \right) \]
\[ BA = B . . . \left( 2 \right)\]
\[ \Rightarrow BAB = BB \left[ \text{Multiplying both sides by} B \right]\]
\[ \Rightarrow BA = B^2 \left[ \text{From eq} . \left( 1 \right) \right]\]
\[ \Rightarrow B = B^2 \left[\text{From eq }. \left( 2 \right) \right]\]
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