Question

Select all statements below which are true for all invertible × matrices and = B. 4 is invertible C. (+)^2=^2+^2+2 D. + is invertible E. (+−1)^9=^9+^−9 F. (−)(+)=−^2

Answer 1

hello your question is poorly written below is the well written question and the options aren't available hence i will provide a general answer

Select all statements below which are true for all invertible n × n matrices. A and B

answer : a)(In+A)(In+A^-1) = In + A^-1 +A +AA^-1 = In + A^-1 +A + In = 2In+A+A^-1.

since (AB)^-1 = B^-1 *A^-1 hence

b) (A^6)^-1 will be (AAAAAA)^-1= (A^-1)( A^-1)( A^-1)( A^-1)( A^-1)( A^-1) = (A-1)6.

Explanation:

The True statements for all invertible n x n matrices A and B are :

(In+A)(In+A^-1) = In + A^-1 +A +AA^-1 = In + A^-1 +A + In = 2In+A+A^-1.

since (AB)^-1 = B^-1 *A^-1 hence (A^6)^-1 will be (AAAAAA)^-1= (A^-1)( A^-1)( A^-1)( A^-1)( A^-1)( A^-1) = (A-1)6.