Consider the following \(3 \times 3\) matrix \([\mathbf{T}]\) :

a. Write the transpose \(\mathbf{T}^{\mathrm{T}}\).

b. Show that the matrix \([\mathbf{S}]=[\mathbf{T}]+[\mathbf{T}]^{\mathrm{T}}\) is a symmetric matrix.

c. Show that the matrix \([\mathbf{A}]=[\mathbf{T}]-[\mathbf{T}]^{\mathrm{T}}\) is a skew-symmetric matrix. What are the diagonal components of the matrix \([\mathbf{A}]\) ?

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[272] [T]= 3 4 5. 6 3 7