Matrices

mun · **Joined:** Fri, 28 Dec 2007 12:01:53 UTC **Posts:** 1261

If A and B are square matrices of order 2 then det(A+B)=0 possible only when
(a)det(A)or det(B)=0
(b)det(A)and det(B)=0
(c)det(A)+det(B)=0
(d)A+B=O(NULL matrices) {where det stands for determinant}
which option is correct

Shadow · **Posted:** Tue, 29 May 2012 20:56:57 UTC

mun wrote:

If A and B are square matrices of order 2 then det(A+B)=0 possible only when
(a)det(A)or det(B)=0
(b)det(A)and det(B)=0
(c)det(A)+det(B)=0
(d)A+B=O(NULL matrices) {where det stands for determinant}
which option is correct

I don't like this question the "only when" is a problem. It doesn't need to be that A=-B

as in option (d), but that certainly is a true time, similarly it can be that det A +det B = 0, but it is not NECESSARILY so, and the same is true for the other options, none of them are "only when"s.

In particular, here is a counterexample to all of them:

$A= \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}$ $B=\begin{pmatrix} -1 & 0 \\ 0 & 5 \end{pmatrix}$

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Matrices

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