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Questions  

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

a
det A=0  and  det B=0
b
det A +det B≠0
c
det A=0  or det B=0
d
None of these

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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