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

Answer 1

B 

\[Here, \] 

\[AB = A . . . \left( 1 \right) \] 

\[ BA = B . . . \left( 2 \right)\] 
\[ \Rightarrow BAB = BB \left[ \text{Multiplying both sides by} B \right]\] 

\[ \Rightarrow BA = B^2 \left[ \text{From eq} . \left( 1 \right) \right]\] 

\[ \Rightarrow B = B^2 \left[\text{From eq }. \left( 2 \right) \right]\]