If B0=⎡⎢⎣−4−3−3101443⎤⎥⎦,Bn=adj(Bn−1),∀n∈N and I is identity matrix of order 3. Then B1+B3+B5+B7+B9 is equal to
A
B0
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B
5B0
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C
25B0
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D
B0+5I
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Solution
The correct option is B5B0 Given : B0=⎡⎢⎣−4−3−3101443⎤⎥⎦
Finding the adjoint of the matrix, we get ⇒adjB0=⎡⎢⎣−414−304−313⎤⎥⎦T⇒adjB0=⎡⎢⎣−4−3−3101443⎤⎥⎦=B0
Now, B1=adj(B0)=B0B2=adj(B1)=B0
Similarly, Bn=B0∀n∈N∴B1+B3+B5+B7+B9=5B0