(a) If I is the 4 4 matrix with every entry 1, show that I -...

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(a) If I is the 4 × 4 matrix with every entry 1, show that I - 1/2 J is self-inverse and symmetric.
(b) If X is n × m and satisfies XTX = lm, show that Im,-2XXT is self-inverse and symmetric.
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