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For a matrix M = \(A= \begin{bmatrix} \frac{3}{5} & \frac{4}{5}\\ x & \frac{3}{5} \\ \end{bmatrix}\)  , the transpose of the matrix is equal to the inverse of the matrix. The value of  \(x\) is given by

(a)    \(-\frac{4}{5}\)                                        (b)    \(-\frac{3}{5}\)

(c)    \(\frac{3}{5}\)                                            (d)    \(\frac{4}{5}\)

Ans.
\(M^t=M^-1\) , means matrix is orthogonal , which means |A|=1

so, \(3/5*3/5-4/5*x=1\)

so, x=-4/5