Hint: In order to determine the value of (A+B)2 , multiply the both side of the given equation B=−A−1BA with the A . Remember that the multiplication of a matrix with its inverse gives the identity matrix. Now expand the (A+B)2 as (A+B)(A+B) .simplify it further and use the result obtained earlier in this expansion to get the required result. Complete step-by-step answer: We are given two square matrices A and B having relation between as B=−A−1BA Since, B=−A−1BA Let's multiply A on both sides of the equation, we get AB=−AA−1BA As we know when a matrix is multiplied with its inverse matrix, it results into identity matrix. So here AA−1=I AB=−IBA AB=−BA⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(1) We have to find the value of (A+B)2, lets rewrite this thing ⇒(A+B)2=(A+B)(A+B) ⇒(A+B)2=A⋅A+A⋅B+B⋅A+B⋅B From the equation (1) AB=−BA, putting this into the above expression we get ⇒(A+B)2=A2−BA+BA+B2 ⇒(A+B)2=A2+B2 Therefore the (A+B)2 is equal to A2+B2 .