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For any 3xx3 matrix M, let abs(M) denote...

For any `3xx3` matrix M, let `abs(M)` denote the determinant of M. Let
`E=[(1,2,3),(2,3,4),(8,13,18)] , P=[(1,0,0),(0,0,1),(0,1,0)] and F=[(1,3,2),(8,18,13),(2,4,3)]`
If Q is a nonsingular matrix of order `3xx3`, then which of the following statements is (are) TRUE ?

A

`F=PEP and P^2=[(1,0,0),(0,1,0),(0,0,1)]`

B

`abs(EQ+PFQ^-1)=abs(EQ)+abs(PFQ^-1)`

C

`abs((EF)^3) gt abs(EF)^2`

D

Sum of the diagonal entries of `P^-1EP+F` is equal to the sum of diagonal entries of `E+P^-1FP`

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