Can you multiply a Matrix (A) by a Matrix (B) to get the transposed of A?

[Anonymous No.11464212]

If so what would be the properties of the Matrix A and B?

[Anonymous No.11464213]

I know this seems like a homework question but I genuinely want to know

[Anonymous No.11464226]

>>11464212
[math]AB=A^T[/math]
[math]B = A^{-1} A^T[/math]
Ask this stuff in sqt, for Christ's sake.

[Anonymous No.11464230]

If there were such a T, we would have [math]T = T X I = I^T = I[/math], where [math]I[/math] is the identity.
But that would mean that [math]A = I X A = T X A = A^T[/math] for all matrices A i.e all matrices are their tranpose.

So no, you can't.

[Anonymous No.11464237]

>>11464212

Linear algebra proofs like this are really easy if you just write down the question in terms of matrix multiplication and use the properties given by your textbook, idk why you'd make a thread.

[Anonymous No.11464277]

>>11464230
He didn't require the B to be the same for all matrices

[Anonymous No.11464282]

>>11464212
is transpose a linear operation?
does it satisfy T(aA + bB) = aT(A) + bT(B)?
if so, then since matricies are finite dimensional vector spaces, then yes, you can construct a matrix to do that.