Let-A-and-B-are-3-3-matrices-The-statements-below-which-is-True-is-A-AB-BA-B-If-AB-0-then-only-A-0-or-B-0-is-true-C-If-AB-I-then-only-A-I-or-A-I-is-true-D-There-exist-A-

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Question Number 35482 by Joel579 last updated on 19/May/18

$$\mathrm{Let}A\mathrm{and}B\mathrm{are}3\times 3\mathrm{matrices}.\mathrm{The}\mathrm{statements}\mathrm{below}$$$$\mathrm{which}\mathrm{is}True\mathrm{is}\dots$$$$\left(\mathrm{A}\right)AB=BA$$$$\left(\mathrm{B}\right)\mathrm{If}AB=0,\mathrm{then}\mathrm{only}A=0\mathrm{or}B=0\mathrm{is}\mathrm{true}$$$$\left(\mathrm{C}\right)\mathrm{If}AB=I,\mathrm{then}\mathrm{only}A=I\mathrm{or}A=-I\mathrm{is}\mathrm{true}$$$$\left(\mathrm{D}\right)\mathrm{There}\mathrm{exist}A\mathrm{where}A\ne 0,\mathrm{and}\mathrm{yet}{A}^2=0$$$$\left(\mathrm{E}\right)\mid A+B\mid =\mid A\mid +\mid B\mid$$

Commented by candre last updated on 19/May/18

$$\mathrm{A}\mathrm{is}\mathrm{false}\mathrm{because}\mathrm{miltiplication}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{comute}\mathrm{in}\mathrm{gemeral}=$$

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