# Two by Two

Algebra Level 3

Consider a 2 by 2 matrix $$C$$ given by $\begin{bmatrix} a & c \\ b & d \end{bmatrix}$ where $$a$$, $$b$$, $$c$$ and $$d$$ are real numbers.

If $$C$$ has the property that its inverse is equal to its transpose, i.e. $$C^{-1}=C^{T}$$, then what is the value of $$a^2+b^2+c^2+d^2$$?

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