SOLUTION: If the matrices A and B are two invertible matrices, then (A + B) is also invertible is this statement true or false and why?

SOLUTION: If the matrices A and B are two invertible matrices, then (A + B) is also invertible is this statement true or false and why?

Algebra.Com

Question 1006562: If the matrices A and B are two invertible matrices, then (A + B) is also invertible

is this statement true or false and why?
Answer by ikleyn(52786) (Show Source): You can put this solution on YOUR website!
.
False.

For a given invertible matrix A take the matrix B as B = -A.

Then B is invertible, and A + B = 0 (zero matrix), which is not invertible.

RELATED QUESTIONS
If A is an invertible 2 x 2 matrix,then A^t is invertible and (At)^-1 = (A^-1)^t. (answered by jim_thompson5910)

If A and B are symmetric matrices and if AB = BA, then AB is symmetric is this... (answered by jim_thompson5910)

Q−1: [5×2 marks] Answer each of the following as True or False justifying your... (answered by math_tutor2020)

Suppose A and B are n × n matrices. If A and B are invertible, then A B is invertible.... (answered by Edwin McCravy)

(a)If A is idempotent and has an inverse A^(-1) show that A=I Explain what this result... (answered by jim_thompson5910)

If (1 2 1) is a solution of matrix equation Ax=B. Determine and explain why is each... (answered by ikleyn)

Assume that all matrices are invertible and solve for the matrix X in: (A^-1 X)^-1 =A... (answered by jim_thompson5910)

Question: Assume A and B are invertible matrices. (a) Find X in the following relation... (answered by user_dude2008)

Give an example of two invertible 2�2 matrices A and B such that (A + B)^I =... (answered by Edwin McCravy)