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Prove that for an n×n matrix A, if A^2 is invertible, then A is invertible.

Question

Prove that for an n×n matrix A, if A^2 is invertible, then A is invertible.

check_circleAnswer
Step 1

Since, if a matrix A is non-zero then A is invertible.

Step 2

Given,

A is a square matrix. Also given that, A is invertible matrix.

Step 3

So that,...

det(A)0
Therefore,
det(A) 0
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det(A)0 Therefore, det(A) 0

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