Answer to Question #160251 in Linear Algebra for Sarita bartwal

Question

The sum of two invertible matrices is an invertible matrix.

True or false.

Answer 1

Solution:

False.

Example: take A=I, B=-I.

Then A is invertible (because every identity matrix, I is invertible). 

B is also invertible because if we multiply an invertible matrix by a non-zero number, we get an invertible matrix.

But A+B=I+(-I)= I-I=O (which is null matrix and not invertible)

Hence, the sum of two invertible matrices is an invertible matrix.