If then A2 is

Engineering

Mathematics

Algebra of Matrices

Multiplication of Matrices

Question

If $A = [\begin{array}{ccc} 2 & 5 & - 3 \\ - 1 & 3 & 1 \\ 4 & 1 & 2 \end{array}]$ then A² is

$[\begin{array}{ccc} - 13 & 22 & - 7 \\ - 1 & 5 & 8 \\ 15 & 25 & - 7 \end{array}]$

$[\begin{array}{ccc} - 13 & 22 & - 7 \\ 15 & 25 & - 7 \\ - 1 & 5 & 8 \end{array}]$

$[\begin{array}{ccc} 13 & 22 & 7 \\ 15 & 25 & - 7 \\ - 1 & 5 & 8 \end{array}]$

$[\begin{array}{ccc} - 13 & 22 & - 7 \\ 15 & 25 & 7 \\ 1 & 5 & 8 \end{array}]$

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A^{2} = A . A = [\begin{array}{ccc} 2 & 5 & - 3 \\ - 1 & 3 & 1 \\ 4 & 1 & 2 \end{array}] . [\begin{array}{ccc} 2 & 5 & - 3 \\ - 1 & 3 & 1 \\ 4 & 1 & 2 \end{array}]

= [\begin{array}{ccc} - 13 & 22 & 2 \times - 3 + 5 \times 1 + (- 3) \times 2 \\ - 1 & 5 & 8 \\ 15 & 25 & - 7 \end{array}]

[\begin{array}{ccc} - 13 & 22 & - 7 \\ - 1 & 5 & 8 \\ - 15 & 25 & - 7 \end{array}]

Hence, B will be correct answer.