Question

Let A = [(2, -1), (3, 4)], B = [(5, 2), (7, 4)], C = [(2, 5), (3, 8)]. Find a matrix D such that CD – AB = O.

Answer 1

Since A, B, C are all square matrices of order 2, and CD – AB is well defined, D must be a square matrix of order 2.

By equality of matrices, we get 

2a + 5c – 3 = 0 ... (1) 

3a + 8c – 43 = 0 ... (2) 

2b + 5d = 0 ... (3) 

and 3b + 8d – 22 = 0 ... (4) 

Solving (1) and (2), we get a = –191, c = 77. 

Solving (3) and (4), we get b = – 110, d = 44.

Therefore