JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If \(A\) and \(B\) are two non-zero \(n \times n\) matrics such that \(A ^2+ B = A ^2 B\), then
- A \(AB = I\)
- B \(A ^2 B = I\)
- C \(A ^2= I\) or \(B = I\)
- D \(A ^2 B = BA ^2\)
Answer & Solution
Correct Answer
(D) \(A ^2 B = BA ^2\)
Step-by-step Solution
Detailed explanation
\(A^2+B=A^2 B\) \(\left(A^2-I\right)(B-I)=I\) \(A^2+B=A^2 B\) \(A^2(B-I)=B\) \(A^2=B(B-I)^{-1}\) \(A^2=B\left(A^2-I\right)\) \(A^2=B A^2-B\) \(A^2+B=B A^2\) \(A^2 B=B A^2\)
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