7. Let A be an invertible matrix. Prove that if A-¹ = AT, then det(A) = ±1. 8. Let x and y be vectors in 3-space, and s

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7 Let A Be An Invertible Matrix Prove That If A At Then Det A 1 8 Let X And Y Be Vectors In 3 Space And S 1 (13.88 KiB) Viewed 34 times

Solve the two proofs (linear alegebra)
7. Let A be an invertible matrix. Prove that if A-¹ = AT, then det(A) = ±1.
8. Let x and y be vectors in 3-space, and suppose u is orthogonal to both x and y. Prove that to k₁x + k₂y, for every pair of scalars k₁ and k₂. is also orthogonal