Let P be a 2×2 matrix such that [10]P=−1√2[11] and [01]P=1√2[−11] If 0 and I denote the zero and identity matrices of order 2, respectively, then which of the following options is correct ?
A
P8−P6+P4+P2=0
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B
P8+P6−P4+P2=I
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C
P8+P6+P4−P2=2I
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D
P8−P6−P4−P2=0
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Solution
The correct option is CP8+P6+P4−P2=2I [10][abcd]=−1√2[11] ⇒[ab]=−1√2[11]