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Please Solve R. D. Sharma class 12 Chapter 4 Algbra of Matrices Exercise Multiple Choice Questions Question  3 Maths textbook Solution.

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Answer: The correct option is \text { (A), } \mathrm{B}^{2}=\mathrm{B}

Given: AB = A, BA = B


It is given that,

AB = A                                                                                                                                   … (1)

BA = B                                                                                                                                   … (2)

Now from Equation (2),

\begin{aligned} &B \times(A B)=B \\ &B^{2} A=B \end{aligned}

Again from Equation (2),

\begin{aligned} &\mathrm{B}^{2} \mathrm{~A}=\mathrm{BA} \\ &\mathrm{B}^{2}=\mathrm{B} \end{aligned}

So, the option (B) is correct.

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