Let A = 2 0 7 0 1 0 1 - 2 1 and B = - k 14 k 7 k 0 1 0 k - 4 k - 2 k . If A B = I , where I is an identity matrix of order 3 , then the sum of all elements of matrix B is equal to

Step-by-step solution

A B = 2 0 7 0 1 0 1 - 2 1    - k 14 k 7 k 0 1 0 k - 4 k - 2 k = 5 k 0 0 0 1 0 0 10 k - 2 5 k A B = I 5 k 0 0 0 1 0 0 10 k - 2 5 k = 1 0 0 0 1 0 0 0 1 ⇒   k = 1 5 Sum of all element of B = 15 k + 1 = 4