COMEDK · Maths · 21. Matrices
\(A\) and \(B\) are two matrices such that \(A B=B\), \(B A=A\), then \(A^{2}+B^{2}=\)
- A \(2 A B\)
- B \(2 B A\)
- C \(A+B\)
- D \(A B\)
Answer & Solution
Correct Answer
(C) \(A+B\)
Step-by-step Solution
Detailed explanation
Given, \(A B=B\) Multiply by \(A\) on both sides \[ A B A=B A \quad \text{...(i)} \] Also, \(B A=A\) Multiply by \(B\) on both sides \[ B A B=A B \quad \text{...(ii)} \] Adding Eqs. (i) and (ii), we get \(A B A+B A B=B A+A B\) \(\Rightarrow \quad A(B A)+B(A B)=B A+A B\)…
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