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For matrices, a mulitplicative identity is a square matrix X such XA = AX = A...

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Advance Math

For matrices, a mulitplicative identity is a square matrix Xsuch XA = AX = A for any square matrix A. Prove that X must be theidentity matrix.

Prove that for any invertible matrix A, the inverse matrix mustbe unique. Hint: Assume that there are two inverses andthen show that they much in fact be the same matrix.

Prove Theorem which shows that Gauss-Jordan Elimination producesthe inverse matrix for any invertible matrix A. Your proof cannotuse elementary matrices (like the book’s proof does).

Prove that null(A) is a vector space.

Prove that col(A) is a vector space.

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