If , then A2 =

Engineering

Mathematics

Introduction to Matrix

Algebra of Matrices

Question

If $A = [\begin{array}{cc} 6 & 9 \\ - 4 & - 6 \end{array}]$ , then A² =

$[\begin{array}{cc} 6 & 9 \\ 4 & - 6 \end{array}]$

$[\begin{array}{cc} 6 & 9 \\ - 4 & 6 \end{array}]$

$[\begin{array}{cc} 0 & 0 \\ 0 & 0 \end{array}]$

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

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We need to find the matrix A² where the given matrix A is $[\begin{array}{cc} 6 & 9 \\ - 4 & - 6 \end{array}]$

A² = A · A

$= [\begin{array}{cc} 6 & 9 \\ - 4 & - 6 \end{array}] [\begin{array}{cc} 6 & 9 \\ - 4 & - 6 \end{array}]$

$= [\begin{array}{cc} 36 - 36 & 54 - 54 \\ - 24 + 24 & - 36 + 36 \end{array}]$

$= [\begin{array}{ll} 0 0 \\ 0 0 \end{array}]$