Q.
Let P 1004101641 and I be the identity matrixof order 3. If Q=qii ] is a matrix such that P50−Q=I then,931+q32q21 equal
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a
52
b
103
c
201
d
205
answer is B.
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Detailed Solution
We have P=1004101641∴P2=PP=10041016411004101641=10081016+3281P3=P2P=10081016+32811004101641=100121016+32+48121By observing the symmetry, we obtain P50=4×5010 16+32+48+…50 terms 4×501⇒ P50=1002001016×50×5122001 ∴ P50−Q=I⇒ Q=P50−I=00020000204002000⇒ q21=200,q31=20400 and q32=200∴ q31+q32q21=20400+200200=20600200=103
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