If A is a matrix, and the system AX=O has a non-trivial solution, show that there is no matrix, B, such that BA=I.

dripcima24

dripcima24

Answered question

2022-09-29

If A is a matrix, and the system AX=O has a non-trivial solution, show that there is no matrix, B, such that BA=I.

Answer & Explanation

Cameron Wallace

Cameron Wallace

Beginner2022-09-30Added 8 answers

If V is a nontrivial solution and B A = I, then
V = I V = ( B A ) V = B ( A V ) = B O = O ,
which contradicts V being nontrivial.
KesseTher12

KesseTher12

Beginner2022-10-01Added 6 answers

𝐴 multiplied on the right by 𝑋 gets 0 and multiplied on the left by 𝐵 gets 𝐼. Multiply on both sides and use associativity, that is, you can first multiply on the right by 𝑋, then on the left by 𝐵, you get the same as: first multiply on the left by 𝐵 then multiply on the right by 𝑋.

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