book Maths Puzzle Numerical Ability

Let T be a linear operator in V. Prove that T^2 = 0 if and only if the range T is a subset of null T.

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book Other Question

evaluate the 3 x 3 determinant


3 4 -1

4 6 2

8 -2 3
log (1 + cos x + i sin x)/(cos x – 1 – i sin x)