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

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Introduction to Matrix

Algebra of Matrices

Question

If matrix A = [a_ij]_2×2, where a_ij * 1 if 1 * j and 0 if i = j then A² is equal to

None of these

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We have, A = [a_ij]_2×2. where a_ij = 1 if 1 ≠ j and if i = j

∴ A = [\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix}]

and

A^{2} = [\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix}] [\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix}] = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] = I