If , then |A + AT| equals

Engineering

Mathematics

Algebra of Matrices

Question

If $A = [\begin{array}{cc} a & b \\ b & a \end{array}]$ , then |A + A^T| equals

4(a² – b²)

2(a² – b²)

(a² – b²)

4ab

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$A + A^{T} = [\begin{array}{cc} a & b \\ b & a \end{array}] [\begin{array}{cc} a & b \\ b & a \end{array}] = [\begin{array}{cc} 2 a & 2 b \\ 2 b & 2 a \end{array}]$
|A + A^T| = 4a² – 4b²
Ans: A