If matrix A = [aij]2 × 2, where aij = 1 if i ≠ j, aij = 0 if i = j then A2 is equal to

  1. I
  2. A
  3. 0
  4. None of these

Answer (Detailed Solution Below)

Option 1 : I

Detailed Solution

Download Solution PDF

Concept:

Identity matrix: A square matrix in which elements in the main diagonal are all '1' and the rest are all zero is called an identity matrix or unit matrix.

Thus, the square matrix A = [aij] where aij={1,ifi=j0,ifij

e.g.[1001][100010001]are identity matrices of order 2 and 3 respectively.

Calculation:

We have A = [aij]2×2, where aij={0,ifi=j1,ifij

∴ A = [0110]

∴  A2 

= A⋅ A

[0110][0110]

[1001]

= I

Get Free Access Now
Hot Links: lotus teen patti teen patti apk teen patti lucky teen patti gold downloadable content teen patti sequence