GATE | GATE CS 1997 | Question 27

Let A= (a_ij) be an n-rowed square matrix and I₁₂ be the matrix obtained by interchanging the first and second rows of the n-rowed Identify matrix. Then AI₁₂ is such that its first
(A) row is the same as its second row
(B) row is the same as the second row of A
(C) column is the same as the second column of A
(D) row is all zero


Answer: (C)

Explanation:
When the above matrices are multiplied, the result is , which is the matrix A with it’s first and second row interchanged.
This is because the first row of has a 1 in the second column and it’s second row has a 1 in the first column. So when the matrices are multiplied, the first and second rows get exchanged.

This explanation is provided by Chirag Manwani.

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