SOLVED: Verily, the following properties use any distinct, invertible A and B. 4x4 upper triangular matrices of your choice:The inverse of an upper triangular matrix is upper triangular; (AB)^-1 = B^-1A^-1, trace(AB), trace(BA), det(AB), det(BA).(BONUS mark) Give an example of matrices B such that det(AB) ≠ det(BA).

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SOLVED:Given two 3x3 similar matrices A and B. Which of the following statements are true? (check all that apply) There is an invertible matrix P such that A = P-IBPA and B must be symmetricA-1 is similar to B-1A and B may represent the same transformation in R3 relative to two different bases. Aand B have the same characteristic polynomial

16 prove that if a is nonsingular then at is nonsingular and at a hint ab btat 83668

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