# 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 \(a^2+b^2+c^2+d^2\)?