What is entry A in the matrix multiplication: ( a) 1 (b) -2(c) 5 (d) 11(e) 13 (f) 0.

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Presentation transcript:

What is entry A in the matrix multiplication: ( a) 1 (b) -2(c) 5 (d) 11(e) 13 (f) 0

What is entry D in the matrix multiplication: ( a) 1 (b) -2(c) 5 (d) 11(e) 13 (f) 0

What is the first sentence of the proof? (a) Assume (G, *) is a group. (b) Assume the identity element is unique. (c) Assume (G *) is not a group. (d) Assume there are three identity elements.

What is the next sentence of the proof? (a) Assume (G, *) is not a group. (b) Assume the identity element is unique. (c) Assume x * e = x. (d) Assume e 1 and e 2 are identity elements.

What is the last sentence of the proof? (a) Therefore, (G, *) is a group. (b) Therefore, e 1 = e 2. (c) Therefore x * e 1 = x. (d) Therefore, e 1 * e 2 = e.

What is the next sentence of the proof? (a) Assume (G, *) is not a group. (b) Assume the inverse is unique. (c) Assume x * x -1 = e. (d) Assume y 1 and y 2 are inverses of x.

What is the last sentence of the proof? (a) Therefore, (G, *) is a group. (b) Therefore, x has an inverse. (c) Therefore x * y 1 = e. (d) Therefore, y 1 = y 2.