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It is not true. Verify that $A=\begin{bmatrix}1&{\;\;1}\\{2}&{-1}\end{bmatrix}$ and $ B=\begin{bmatrix}{1}&{2}\\{2}&{1}\end{bmatrix}$ are invertible and diagonalzable matrices on $\mathbb{R}$, however $AB=\begin{bmatrix}{3}&{3}\\{0}&{3}\end{bmatrix}$ it is not diagonalizable.if A and B are both invertible and diagonalizable matrices (from the same order), is A*B a diagonalizable matrix ? why ?
Not always. But when A,B are interchangable, i.e., AB=BA, then AB IS diagonalizable since then A and B are simultaneously diagonalizable, i.e., we can find the same invertible matrixHello
I have a little question
if A and B are both invertible and diagonalizable matrices (from the same order), is A*B a diagonalizable matrix ? why ?
I have not got a clue...
thanks !