Let A = a i j 1 ≤ i , j ¯ 3 be a 3 × 3 invertible matrix where each a i i is a real number. Denote the inverse of the matrix A by A - 1 . If ∑ i t l 3 a i j = 1 for 1 ≤ i ≤ 3 , then

Question

Let A = a i j 1 ≤ i , j ¯ 3 be a 3 × 3 invertible matrix where each a i i is a real number. Denote the inverse of the matrix A by A - 1 . If ∑ i t l 3 a i j = 1 for 1 ≤ i ≤ 3 , then, sum of the diagonal entries of A is 1, sum of each row of A - 1 is 1, sum of each row and each column of A - 1 is 1, sum of the diagonal entries of A - 1 is 1

MARKS App · Accepted Answer

Sum of elements in each row of A is 1 . So, A 1 1 1 = 1 1 1 ⇒ A - 1 A 1 1 1 = A - 1 1 1 1 ⇒ 1 1 1 = A - 1 1 1 1 ⇒ sum of elements in each row of A - 1 is 1

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