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Scalar Matrix

If A is a squ...

Question

If A is a square matrix of order 3 such that $A^{3} = I a n d (A + I)^{3} + (A - I)^{3} - 6 A = B$ where I is identity matrix of order 3, then

A

|B| = 2

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B

|B| = 3

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C

|B| = 4

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D

|B| = 8

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Solution

The correct option is D |B| = 8
$A^{3} = I (A + I)^{3} + (A - I)^{3} - 6 A = B \Rightarrow B = 2 A^{3} \Rightarrow B = 2 I ∴ | B | = 2 (4) = 8$

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