If and , verify that (A + B) = (B + A).

Engineering

Mathematics

Algebra of Matrices

Question

If $A = [\begin{array}{ccc} 2 & - 3 & 5 \\ - 1 & 0 & 3 \end{array}]$ and $B = [\begin{array}{ccc} 3 & 2 & - 2 \\ 4 & - 3 & 1 \end{array}]$ , verify that (A + B) = (B + A).

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

$B = [\begin{array}{ccc} 3 & 2 & - 2 \\ 4 & - 3 & 1 \end{array}]$

now,

$A + B = [\begin{array}{ccc} 2 + 3 & - 3 + 2 & 5 - 2 \\ - 1 + 4 & 0 - 3 & 3 + 1 \end{array}] = [\begin{array}{ccc} 5 & - 1 & 3 \\ 3 & - 3 & 4 \end{array}]$

also,

$B + A = [\begin{array}{ccc} 3 + 2 & 2 - 3 & - 2 + 5 \\ 4 - 1 & - 3 + 0 & 1 + 3 \end{array}] = [\begin{array}{ccc} 5 & - 1 & 3 \\ 3 & - 3 & 4 \end{array}]$

Hence, (A + B) = (B + A)