If A is invertible, then

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Name: If A is invertible, then .
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Question

If A is invertible, then 
  
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Quizplus · Accepted Answer

If A is invertible, then it has an inverse matrix B such that AB = BA = I, where I is the identity matrix. Therefore, for any non-zero vector x, we have Ax ≠ 0, and we can multiply both sides by B to get x = IBx = B(Ax), which implies that B is also invertible and (A⁻¹)(B⁻¹) = (AB)⁻¹ = I⁻¹ = I.

If a Is Invertible, Then