Find : A2 if

Engineering

Mathematics

Introduction to Matrix

Algebra of Matrices

Multiplication of Matrices

Question

Find : A² if $A = [\begin{array}{ccc} 1 & 3 & 2 \\ - 5 & 1 & 0 \\ 1 & 2 & 5 \end{array}]$

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A = [\begin{array}{ccc} 1 & 3 & 2 \\ - 5 & 1 & 0 \\ 1 & 2 & 5 \end{array}]

A^{2} = [\begin{array}{ccc} 1 & 3 & 2 \\ - 5 & 1 & 0 \\ 1 & 2 & 5 \end{array}] [\begin{array}{ccc} 1 & 3 & 2 \\ - 5 & 1 & 0 \\ 1 & 2 & 5 \end{array}]

= [\begin{array}{ccc} 1 - 15 + 2 & 3 + 3 + 4 & 2 + 0 + 10 \\ - 5 - 5 + 0 & - 15 + 1 + 0 & - 10 + 0 + 0 \\ 1 - 5 + 1 & 3 + 2 + 10 & 2 + 0 + 25 \end{array}]

= [\begin{array}{ccc} - 12 & 10 & 12 \\ - 10 & - 14 & - 10 \\ - 3 & 15 & 27 \end{array}]