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Matrices and Determinants question

2006 · Shift 0 · Q59

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JEE Main
Mathematics
Matrices and Determinants
2006 · Shift 0 · Q59

Matrices and Determinants question

2006 · Shift 0 · Q59

JEE MainMathematicsMatrices and DeterminantsMCQ+4 / −1

If

A

and

B

are square matrices of size

n\, \times \,n

such that

{A^2} - {B^2} = \left( {A - B} \right)\left( {A + B} \right),

then which of the following will be always true?

A
$A=B$
B
$AB=BA$
C
either of $A$ or $B$ is a zero matrix
D
either of $A$ or $B$ is identity matrix

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