  We present a collection of matrix valued shape invariant potentials which
give rise to new exactly solvable problems of SUSY quantum mechanics. It
includes all irreducible matrix superpotentials of the generic form
$W=kQ+\frac1k R+P$ where $k$ is a variable parameter, $Q$ is the unit matrix
multiplied by a real valued function of independent variable $x$, and $P$, $R$
are hermitian matrices depending on $x$. In particular we recover the
Pron'ko-Stroganov "matrix Coulomb potential" and all known scalar shape
invariant potentials of SUSY quantum mechanics.
  In addition, five new shape invariant potentials are presented. Three of them
admit a dual shape invariance, i.e., the related hamiltonians can be factorized
using two non-equivalent superpotentials. We find discrete spectrum and
eigenvectors for the corresponding Schroedinger equations and prove that these
eigenvectors are normalizable.
