  We use isomorphism $\varphi$ between matrix algebras and simple orthogonal
Clifford algebras $\cl(Q)$ to compute matrix exponential ${e}^{A}$ of a real,
complex, and quaternionic matrix A. The isomorphic image $p=\varphi(A)$ in
$\cl(Q),$ where the quadratic form $Q$ has a suitable signature $(p,q),$ is
exponentiated modulo a minimal polynomial of $p$ using Clifford exponential.
Elements of $\cl(Q)$ are treated as symbolic multivariate polynomials in
Grassmann monomials. Computations in $\cl(Q)$ are performed with a Maple
package `CLIFFORD'. Three examples of matrix exponentiation are given.
