If and . Then find A2

Engineering

Mathematics

Introduction to Matrix

Algebra of Matrices

Multiplication of Matrices

Question

If $A = [\begin{array}{cc} 1 & 3 \\ - 3 & 2 \end{array}]$ and $B = [\begin{array}{cc} - 2 & 1 \\ - 3 & 2 \end{array}]$ . Then find A² – 5B².

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A = [\begin{array}{cc} 1 & 3 \\ - 3 & 2 \end{array}] B = [\begin{array}{cc} - 2 & 1 \\ - 3 & 2 \end{array}]

A^{2} = [\begin{array}{cc} 1 & 3 \\ - 3 & 2 \end{array}] [\begin{array}{cc} 1 & 3 \\ - 3 & 2 \end{array}] . [\begin{array}{cc} 1 - 9 & 3 + 6 \\ - 3 - 6 & - 9 + 4 \end{array}] = [\begin{array}{cc} - 8 & 9 \\ - 9 & - 5 \end{array}]

B^{2} = [\begin{array}{cc} - 2 & 1 \\ - 3 & 2 \end{array}] [\begin{array}{cc} 4 - 3 & - 2 + 2 \\ 6 - 6 & - 3 + 4 \end{array}]

= [\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}]

A^{2} - 5 B^{2} = [\begin{array}{cc} - 8 & 9 \\ - 9 & - 5 \end{array}] - 5 [\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}]

= [\begin{array}{cc} - 8 & 9 \\ - 9 & - 5 \end{array}] - [\begin{array}{cc} 5 & 0 \\ 0 & 5 \end{array}]

= [\begin{array}{cc} - 13 & 9 \\ - 9 & - 10 \end{array}]