#### George Saliaris

##### New member

- Joined
- Dec 15, 2019

- Messages
- 43

If A (n x n) matrix

B (n x b) matrix

AA^T = ΒΒ^Τ = I

Prove that:

det[(A^T *B) - (B^T * A)] = det[A^2 - B^2]

I proved that AB = BA but apart from that I am doing a bunch of useless algebra and thus I am stuck.. Could somebody give me an insight? Ty

P.S1 : It's not a homework exercise/extra credit etc. I am doing in order to practice in determinants

PS2 : I found this online and I thought It could be solved with determinant properties, inverse matrix and properties and the fact that (AB) ^ T =B^T * A^T and not something else.. Correct me If I am wrong..

B (n x b) matrix

AA^T = ΒΒ^Τ = I

Prove that:

det[(A^T *B) - (B^T * A)] = det[A^2 - B^2]

I proved that AB = BA but apart from that I am doing a bunch of useless algebra and thus I am stuck.. Could somebody give me an insight? Ty

P.S1 : It's not a homework exercise/extra credit etc. I am doing in order to practice in determinants

PS2 : I found this online and I thought It could be solved with determinant properties, inverse matrix and properties and the fact that (AB) ^ T =B^T * A^T and not something else.. Correct me If I am wrong..

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