Consider a matrix A with block matrices as follows: A = [A_11 A_12 0 A_22] It can be shown that the inverse of A can be calculated by inverse of submatrices if A11, and A22 are squared matrices: A^-1 = [A_11 A_12 0 A_22]^-1 = [A^-1_11 -A^-1_11 A_12 A^-1_22 0 A^-1_22] Now consider a Matrix A with following submatrices: A11 = identity matrix A22 = identity matrix A12 = [1 2 3;4 5 - 1] Write a code that check the identity shown above: steps are: a) Takes 4 sub matrices: A11, A22, A21, A12 b) Given the information about the matrix A, construct A: a. What is the size of A? (create a zero matrix with that size) c) create a variable LHS which uses matlab built-in function to take the inverse (calculate LHS) d) create a variable RHS which reconstruct the inverse given in the right hand side of the identity e) show that they are equal Consider a matrix A with block matrices as follows: A = [A_11 A_12 0 A_22] It can be shown that the inverse of A can be calculated by inverse of submatrices if A11, and A22 are squared matrices: A^-1 = [A_11 A_12 0 A_22]^-1 = [A^-1_11 -A^-1_11 A_12 A^-1_22 0 A^-1_22] Now consider a Matrix A with following submatrices: A11 = identity matrix A22 = identity matrix A12 = [1 2 3;4 5 - 1] Write a code that check the identity shown above: steps are: a) Takes 4 sub matrices: A11, A22, A21, A12 b) Given the information about the matrix A, construct A: a. What is the size of A? (create a zero matrix with that size) c) create a variable LHS which uses matlab built-in function to take the inverse (calculate LHS) d) create a variable RHS which reconstruct the inverse given in the right hand side of the identity e) show that they are equal