If and then the cofactor of a21 in AB is :

Engineering

Mathematics

Introduction to Matrix

Algebra of Matrices

Transpose and Adjoint of a Matrix

Question

If $A = {\begin{cases} 1 & 4 \\ 2 & 8 \end{cases}}$ and $B = {\begin{cases} x & y \\ y & x \end{cases}}$ then the cofactor of a₂₁ in AB is :

– y – 4x

2x + 8y

– 2x – 8y

y + 4x

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Given $A = (\begin{array}{cc} 1 & 4 \\ 2 & 8 \end{array})$ and $B = (\begin{array}{cc} x & y \\ y & x \end{array})$
So, By operation of multiplication,
$AB = (\begin{array}{cc} x + 4 y & y + 4 x \\ 2 x + 8 y & 2 y + 8 x \end{array})$

So, By property of minor (2),
M₂₁ = minor of a₂₁ = |2x + 8y|
So, cofactor of a₂₁ = M₂₁(– 1)²⁺¹ = – M₂₁ = – 2x – 8y