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Let \(A\) and \(B\) be \(n\times n\) real matrices. Which of the following statements is correct?

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Remember the fundamental rank inequality: \[ rank(A+B)\le rank(A)+rank(B) \] and \[ rank(AB)\le \min\{rank(A),rank(B)\}. \] These two formulas are among the most frequently used results in matrix theory.

Updated On: Jun 25, 2026

\(rank(A+B)=rank(A)+rank(B)\)
\(rank(A+B)\le rank(A)+rank(B)\)
\(rank(A+B)=\min\{rank(A),rank(B)\}\)
\(rank(A+B)=\max\{rank(A),rank(B)\}\)

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The Correct Option is B

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Show Hint

The Correct Option is B

Solution and Explanation

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