Question 6 Give an example of a nonzero 2x3 matrix A and a nonzero 3x2 matrix B. Use your chosen A and B to find the product AB. What is its size? (It will be very surprising if two people get the same answers.) [4] Question 7 State whether the following are true or false. If it is true then you must prove the result. If it is false then you must give an example to show why this is not true. 7.1 If A and B are n x n matrices then (A + B) 2 = A2 + 2AB + B2 . [2] 7.2 (AT ) T = A. [2] 7.3 (A−1 ) −1 = A. [2] 7.4 The transpose of an upper triangular matrix is an upper triangular matrix. [2] 7.5 An upper triangular matrix that is symmetric is a diagonal matrix. [2] [10

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