The classical Polya-Vinogradov inequality gives a bound (roughly of size square root of $p$) on the sum of values of a Dirichlet character modulo $p$ along a segment which is independent of the length of the segment. The proof uses Fourier Analysis on finite abelian groups. Instead of Dirichlet characters which are nothing but characters of the mutiplicative group $\mathrm{GL}(1, \mathbb{F}_p)$ of invertible elements in $\mathbb{F}_p$, the finite field of p elements, we can work with representations of the group $\mathrm{GL}(n, \mathbb{F}_p)$ for $n >1$ and try to generalise the result. I shall describe my joint work with C.S. Rajan on this question and our result for the case $n=2$. As an application, we will describe a matrix analogue of the problem of estimating the least primitive root modulo a prime.