Questions. (1) (5 marks) True or False? Justify your answer. Answers without correct justification will receive no credit." (a) Let A, B, and C be two square matrices of the same dimension and A be an invertible matrix then (A BCA) 2023 - A-1 B2023 2023 A. O True O False Justification: (b) Let A be an n xn matrix. The set of all n x n matrices X that satisfies (A2 -31)X = O is not be closed under the matrix addition. O True O False Justification:(c) If A and B are 6 x 6 matrices of rank 6, then AB also has rank 6. True O False Justification: (d) If A is a 5 x 6 matrix of rank 3, then the solutions of Ax = 0 is has two parameters. O True O False Justification: (e) Matrix 2 3 in Z5 has two distinct eigenvalues. O True O False Justification:(2) (9 marks) Consider the following matrices 0 1 0 B = 0 2 3 Co NO ( Entries of C are from Zg). O CT N 0 Note that only the entries of matrix C are in Zo. The other two matrices A and B are matrices with real numbers entries. (a) Find the inverse of all the given matrices, if they are invertible, using Gauss-Jordan method? Invertibility of A: Invertibility of B: Invertibility of C:(1)) Write the inverse of the given matrices as the product of elementary matrices (Find a sequence of elementary matrices Whose product in a correct order is equal to inverse matrix). For A: For B: For C