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Question

Let P be a 2×2 matrix such that [10]P=12[11] and [01]P=12[11]
If 0 and I denote the zero and identity matrices of order 2, respectively, then which of the following options is correct ?

A
P8P6+P4+P2=0
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B
P8+P6P4+P2=I
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C
P8+P6+P4P2=2I
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D
P8P6P4P2=0
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Solution

The correct option is C P8+P6+P4P2=2I
[10][abcd]=12[11]
[ab]=12[11]

[01][abcd]=12[11]

[cd]=12[11]
[abcd]=⎢ ⎢ ⎢ ⎢12121212⎥ ⎥ ⎥ ⎥P=12[1111]P2=12[2002]P2=IP4,P6,P8=IP8+P6+P4P2=2I

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