If A is an Involuntary matrix and I is a unit matrix of same order, then (I − A) (I + A) is

Question

Question

Answer 1

Concept:

Involuntary matrix:

Matrix A is said to be Involuntary if A² = I, where I is an Identity matrix of same order as of A.
Involuntary matrix is a matrix that is equal to its own inverse. ⇔ A^-1 = A

Calculation:

Given that A is involuntary matrix,

⇒ A² = I

Now,

(I − A) (I + A) = I² – IA + AI − A²

⇒ I – A + A – I (∵ A2 = I)

⇒ 0

∴ (I − A) (I + A) is zero matrix.

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