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Question:

Prove that the determinant of the product of two general 2x2 matrces is the product of their determinants.

What I think is that I should come up with two 2x2 matrices.

1 2 2 3 12 15

3 4 and 5 6 multiply them together and get 26 33

The determinant of the product matrix is six. The determinat of the first matrix is -2 and the second one is -3. Multiply -2 times -3 and that is 6. So I proved that the determinant of the product of the two matrices is the product of their determinants.

Is this right?

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