mat /= float and mat *= float are defined for matrices. But its unclear why other component-wise built-in functions like mix aren't. Seems like they easily could be. Would be useful and shorten shader code.
Code :mat3 m1 = mat3(1); mat3 m2 = mat3(1); mat3 m3 = mix( m1, m2, 0.5 );
Code :tst_vert.glsl(100) : error C1115: unable to find compatible overloaded function "mix(mat3, mat3, float)"