If . Find A2

Engineering

Mathematics

Multiplication of Matrices

Symmetric and Skew Symmetric Matrices

Question

If $A = [\begin{array}{ccc} 3 & 2 & 0 \\ 1 & 4 & 0 \\ 0 & 0 & 5 \end{array}]$ . Find A²

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A^{2} = A . A = [\begin{array}{ccc} 3 & 2 & 0 \\ 1 & 4 & 0 \\ 0 & 0 & 5 \end{array}] [\begin{array}{ccc} 3 & 2 & 0 \\ 1 & 4 & 0 \\ 0 & 0 & 5 \end{array}]

= [\begin{array}{ccc} 3 \times 3 + 2 \times 1 + 0 \times 0 & 3 \times 2 + 2 \times 4 + 0 \times 0 & 3 \times 0 + 2 \times 0 + 0 \times 5 \\ 1 \times 3 + 4 \times 1 + 0 \times 0 & 1 \times 2 + 4 \times 4 + 0 \times 0 & 1 \times 0 + 4 \times 0 + 0 \times 5 \\ 0 \times 3 + 0 \times 1 + 5 \times 0 & 0 \times 2 + 0 \times 4 + 5 \times 0 & 0 \times 0 + 0 \times 0 + 5 \times 5 \end{array}]

= [\begin{array}{ccc} 9 + 2 + 0 & 6 + 8 + 0 & 0 + 0 + 0 \\ 3 + 4 + 0 & 2 + 16 + 0 & 0 + 0 + 0 \\ 0 + 0 + 0 & 0 + 0 + 0 & 0 + 0 + 25 \end{array}]

= [\begin{array}{ccc} 11 & 14 & 0 \\ 7 & 18 & 0 \\ 0 & 0 & 25 \end{array}]

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