Let A and B be two n x n matrices. Call A and B simultaneously diagonalizable, if there is a single matrix X and two diagonal matrices DA and DB so that A = X^-1 DA X and B = X^-1 DB X. Show that if A and B are simultaneously diagonalizable, then A and B commute, that is AB = BA.

Q: Find two 3x3 invertible matrices A and B, such that A+B is not invertible.

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A: Transpose of a matrix is obtained by interchanging the rows into columns and columns into rows.

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A: Topic: matrix multiplication

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A: Let B be an n × m matrix whose columns are linearly independent. To Show:  B has a left inverse.

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A: Let's find.

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A: Please check step 2 for the solution.!

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A: Answer :

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