Suppose are real matrices with .

Then .

Then .

We have to find out whether the statement is true or false.

TIFR GS 2019, Part B Problem 5

Linear Algebra

Medium

Linear algebra, Friedberg, Insel

Do you really need a hint? Try it first!

Can you try it with diagonal matrices with or non-zero diagonal entries?

Consider with all zero entries except and (). is all zeros except (). , thus and has rank .

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