Invertible Matrix A & B: True Formulas

[NeonVomitt]

Which of these formulas hold for all invertible n x n matrices A and B:

1) 8A is invertible
2) A + B is invertible
3) (A + B)^2 = A^2 + B^2 + 2AB
4) (ABA^1)^7 = AB^7A^1
5) (AB)^-1 = A^-1B^-1
6) ABA^-1 = B

Thanks

 

[John Creighto]

Which of these formulas hold for all invertible n x n matrices A and B:

1) 8A is invertible
2) A + B is invertible
3) (A + B)^2 = A^2 + B^2 + 2AB
4) (ABA^1)^7 = AB^7A^1
5) (AB)^-1 = A^-1B^-1
6) ABA^-1 = B

Thanks

For 1 and 2, why not see if you can find the inverse?

For 3 multiply it out fist and tell me what you think

For 4 multiply it out and it should be obvious.

For 5 I'm sure you must have proved something for the left hand side. when you remove the brackets. How does it look like the right hand side?

For 6 Right multiply by A. What did you learn about weather matrices commute?

 

[matt grime]

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