Question

If A=[aᵢⱼ] is a square matrix of order 2 such that aᵢⱼ={1 when i≠j

{0 when i=j ,

then A² is:

A. [ 1 0 ]
[ 1 0 ]
B. [ 1 1 ]
[ 0 0 ]
C. [ 1 1 ]
[ 1 0 ]
D. [ 1 0 ]
[ 0 1 ]

Answer 1

The square of the given 2x2 matrix A, where diagonal elements are 0 and non-diagonal elements are 1, results in the identity matrix of order 2, which is option D. [1 0] [0 1].

Step-by-step explanation:

The question involves determining the square of a given 2x2 matrix A where the elements satisfy a certain condition. The matrix A is such that its diagonal elements are 0 and the non-diagonal elements are 1. To find A squared (A2), we need to perform matrix multiplication of A with itself.

Matrix A is defined as:

A = [0 1]
[1 0]

To find A2, we do the following multiplication:

A2 = A * A = [0*0 + 1*1 0*1 + 1*0]
[1*0 + 0*1 1*1 + 0*0] = [1 0]
[0 1]

Therefore, the correct answer is D. [1 0] [0 1] which is the identity matrix of order 2.