algebraic manipulation - Expressing a matrix in terms of four basis matrices

I have five matrices and I want to represent one in the basis of other four. So how do I find the value of coefficients?

For example, if the matrices are I1, I2, I3, I4, T and the relation between them is

T = (a*I1) + (b*I2) + (c*I3) + (d*I4)

Now to determine the value of coefficients a, b, c, d, what do I have to do in Mathematica?

I have tried this

Solve[{T - a*I1 - b*I2 - c*I3 - d*I4 == 0}, {a, b, c, d}]

but it is showing this error:

Solve::svars: Equations may not give solutions for all "solve" variables.