MatricesHard

Question

If A is a non-singular matrix and B is any matrix satisfying AB - BA = A, then -

Options

A.|B| = 0
B.|A| = 1
C.|B + I| = |B - I|
D.|B| = 1

Solution

AB = BA + A ⇒ |B| = |B + I|
& AB - A = BA ⇒ |B - I| = |B|
∴ |B + I| = |B - I|

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