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SOLVED:Show that all matrices similar to an invertible matrix are invertible. More generally, show that similar matrices have the same rank.

Ex. (5) Show that matrix \left[\begin{array}{lll}0 & 0 & 1 \\ 0... | Filo

SOLVED: Question 1. (5 points Give examples of matrices A and B such that(a) A B is not invertible; although A and B are invertible (6) A B is invertible, although A and B are not invertible.(c) all of A,B, and A B are invertible(d) How many 2 by 2 matrices are there whose entries are ls and Os?(e) Suppose 3 of the 4 entries in a 2 by 2 matrix are ls and the fourth entry is 0 Is this matrix invertible?