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Question

Let P=1004101641 and I be the identity matrix of order 3. If Q=[qij] is a matrix, such that p50Q=I, then q31+q32q21 equals

A
52
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B
103
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C
201
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D
205
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Solution

The correct option is B 103
P=1004101641

P2=10041016411004101641=1008104881

P3=10081048811004101641=100121056121

P4=10081048811004101641=1001610160161


P50=1004×5010p314×501Q=q11q12q13q21q22q23q31q32q33

P50Q=100010001

4×50q21=0

p31q31=0

4×50q32=q

On observing,
p311=16×1

p312=16×(1+2)

p313=16×(1+2+3)

p3150=16×(1+2+3+.....50)

=16×50×512

q31+q32q21=p31+p32p21

=16×25×51+4×504×50

=103

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