Question

6. Let A and B be nxn matrices . Compute (A + B) (A + B). Explain all steps.

Answer 1

(A+B)(A+B)=A.A+B.A+A.B+B.B

Explanation:

Given that matrices A and B are nxn matrices

We need to find (A+B)(A+B)

For understanding the multiplication of matrices let'take A is mxn and B is pxq matrices,we can multiple only when n=p,so our Ab matrices will be mxq.

We know that that in matrices AB is not equal to BA.

Now find

(A+B)(A+B)=A.A+B.A+A.B+B.B

So from we can say that (A+B)(A+B) is not equal to A.A+2B.A+B.B because AB is not equal to BA in matrices.

So (A+B)(A+B)=A.A+B.A+A.B+B.B