If A and B are any 2×2 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

None of these

answer is B.

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Detailed Solution

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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