Question: For a real number a, let 1 Ba = 0 1 1 O 0 an invertible matrix. (a) Find Baby row reducing the augmented matrix

For a real number a, let 1 Ba = 0 1 1 O 0 an invertible matrix. (a) Find Baby row reducing the augmented matrix Ba |13 , and use your answer to show that Ba + Ba does not depend on a. (b) Let P be an invertible 3 x 3 matrix, and let Ca = P-1B. P. Show that P-1BP is inverse to Ca. Hint: Multiply the two matrices together and see what you get. Remember that matrix multiplication is not com- mutative, so if your answer relies on equalities of the form XY = YX, you will lose marks. (c) Use part (b) to show that Ca + C' does not depend on a. (It does depend on P, however.)

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