Consider the following in respect of two non-singular matrices A and B of same order: 1. det (A+B)= det A+ det B 2. (A+B)⁻¹=A⁻¹+B⁻¹ Which of the above is/are correct?

Step-by-step solution

Non-singular matrix is a matrix whose determinate Value is non-zero. Let A= [ array ll 1 & 1 1 & 2 array ] and B= [ array ll 2 & 1 1 & 2 array ] Here, A and B are non-singular matrix Now from Statement 1: aligned & A+B= [ array ll 1 & 1 1 & 2 array ]+ [ array ll 2 & 1 1 & 2 array ]= [ array ll 3 & 2 2 & 4 array ] & det (A+B)=12-4=8 & Now det (A)= | array ll 1 & 1 1 & 2 array |=1 & and det (B)= | array ll 2 & 1 1 & 2 array |=3 aligned Now, det (A+B)=4 det (A+B) Statement 1 is wrong. Now from Statement 2: aligned & (