1
GATE IN 2006
MCQ (Single Correct Answer)
+2
-0.6
For a given $$2x2$$ matrix $$A,$$ it is observved that $$A\left[ {\matrix{ 1 \cr { - 1} \cr } } \right] = - 1\left[ {\matrix{ 1 \cr { - 1} \cr } } \right]$$ and
$$A\left[ {\matrix{ 1 \cr { - 2} \cr } } \right] = - 2\left[ {\matrix{ 1 \cr { - 2} \cr } } \right]$$ then the matrix $$A$$ is
A
$$A = \left[ {\matrix{ 1 & 1 \cr { - 1} & { - 2} \cr } } \right]\,\,\left[ {\matrix{ 1 & 0 \cr 1 & 2 \cr } } \right]\,\,\left[ {\matrix{ 2 & 1 \cr { - 1} & { - 1} \cr } } \right]$$
B
$$A = \left[ {\matrix{ 1 & 1 \cr { - 1} & { - 2} \cr } } \right]\,\,\left[ {\matrix{ 1 & 0 \cr 1 & 2 \cr } } \right]\,\,\left[ {\matrix{ 2 & 1 \cr { - 1} & { - 1} \cr } } \right]$$
C
$$A = \left[ {\matrix{ 1 & 1 \cr { - 1} & { - 2} \cr } } \right]\,\,\left[ {\matrix{ { - 1} & 0 \cr 0 & { - 2} \cr } } \right]\,\,\left[ {\matrix{ 2 & 1 \cr { - 1} & { - 1} \cr } } \right]$$
D
$$A = \left[ {\matrix{ 0 & { - 2} \cr 1 & { - 3} \cr } } \right]$$
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