If and and AB = I3, then x + y = ____

Engineering

Mathematics

Introduction to Matrix

Algebra of Matrices

Question

If $A = [\begin{array}{ccc} 1 & 2 & x \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}]$ and $B = [\begin{array}{ccc} 1 & - 2 & y \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}]$ and AB = I₃, then x + y = _____.

None of these

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$A = [\begin{array}{ccc} 1 & 2 & x \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}], B = [\begin{array}{ccc} 1 & - 2 & y \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}]$

$AB = [\begin{array}{lll} 1 0 y + x \\ 0 1 0 \\ 0 0 1 \end{array}]$

∴ y + x = 0