Let A be a non-singular symmetric matrix of order 3 . If A T = A 2 - I , then A - I - 1 is equal to

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Question: Answered & Verified by Expert

Let

A

be a non-singular symmetric matrix of order

3

. If

A^{T} = A^{2} - I

, then

{(A - I)}^{- 1}

is equal to

MathematicsMatricesJEE Main

Options:

A $A$
B $2 A$
C $A - I$
D $2 A - I$

Solution:

1702 Upvotes Verified Answer

The correct answer is:

A

∵ A^{T} = A

(as

A

is symmetric)

∴ A = A^{2} - I \Rightarrow A^{2} - A = I

\Rightarrow I = A (A - I) = (A - I) A

\Rightarrow {(A - I)}^{- 1} = A

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