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If A and B are different matrices satisf...

If `A` and `B` are different matrices satisfying `A^(3) = B^(3)` and
`A^(2) B = B^(2) A`, then

A

`det (A^(2) + B^(2))` must be zero

B

det `(A-B)` must be zero

C

`det (A^(2) + B^(2))` as well as `det (A - B)` must be zero

D

alteast one of `det (A^(2) + B^(2))` or `det (A - B)` must be zero

Text Solution

Verified by Experts

The correct Answer is:
D
`because A^(3) - A^(2) B = B^(3) - B^(2) A `
`rArr A^(2) (A-B) = B^(2)(B-A)`
or `(A^(2) + B^(2)) (A-B) =0`
or det `(A^(2)+B^(2)) cdot det (A-B) = 0`
Either det `(A^(2) + B^(2)) = 0` or det `(A-B) = 0`
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