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(Solved): Problem 4 Let A and B be two 3\times 3 matrices satisfying the following conditions: AB=OO denotes t ...
Problem 4
Let A and B be two 3\times 3 matrices satisfying the
following conditions:
AB=OO denotes the 3\times 3 zero matrix(A+2B)(2A-B)=I
Which of the following statements is not true?
(a) A=O.
(b) BA=O.
A+2B=(2A-B)^(-1)
(b) BA=O.
2A-B=((A+2B)^(-1))/(A^(-1)+2B^(-1))
(c) A+2B is invertible.
(d) A+B is invertible.
(e) B=O, if A^(2)+B^(2)=(1)/(2)I.