Question

Select all statements below which are true for all invertible × matrices and A. (−1)2=2−1 B. is invertible C. 7 is invertible D. −1= E. ( −1)4=4 −4 F. ( )(−)=2−2


which ones are true?

Answer 1

Step-by-step explanation:

Let's analyze each statement:

A. \( (-1)^2 = 2^{-1} \) - This is false. \( (-1)^2 = 1 \), not \( 2^{-1} = \frac{1}{2} \).

B. A is invertible - This statement doesn't provide enough information to determine its truth value. We need to know more about matrix A to determine if it's invertible or not.

C. 7 is invertible - This statement is false. 7 is not an invertible number because it doesn't have a multiplicative inverse.

D. \( -1 = 1 \) - This statement is false. \( -1 \) is not equal to \( 1 \).

E. \( (-1)^4 = 4^{-4} \) - This is false. \( (-1)^4 = 1 \), not \( 4^{-4} = \frac{1}{256} \).

F. \( ()(-) = 2^{-2} \) - This statement is incomplete. Without knowing what is represented by the empty parentheses, we can't determine its truth value.

So, the true statements are: None of the statements provided are true.