If A and B are any $$2$$×$$2$$ matrices, then det $$(A+B)=0$$ implies

Correct option is 2det A +det B≠0

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If A and B are any $2 \times 2$ matrices, then $\det (A + B) = 0$ implies

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det A=0 and det B=0

det A +det B≠0

det A=0 or det B=0

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detailed solution

Correct option is B

Let A=[1−110] and B=[−11−10] ⇒ A+B=[0000] ∴ det(A+B)=0 But det A=1, det B=1, ∴ det A≠0, det B≠0 ∴ det (A+B)≠det A+det B

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If A and B are any 2×2 matrices, then det (A+B)=0 implies

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If A and B are any $2 \times 2$ matrices, then $\det (A + B) = 0$ implies