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Finding Inverse Using Elementary Transformations

If A and B ar...

Question

If A and B are square matrices of order 3 such that $(A + B) (A - B) = A^{2} - B^{2}$ , then $(A B A^{- 1})^{2}$ is -

A^{2} B^{2}

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A^{2}

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B^{2}

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I

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Solution

The correct option is C $B^{2}$
$A B = B A$

So $A B A^{- 1} = B A A^{- 1} = B$

$(A B A^{- 1})^{2} = B^{2}$

Suggest Corrections

Similar questions

A

B

(A + B) (A - B) = A^{2} - B^{2}

(A B A^{- 1})^{2}

A^{2} - B^{2} = (A - B) (A + B)

A

B

n \times n

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

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A^{2} = A, B^{2} = B, A B = B A = 0

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