Clifford and Grassmann algebras are considered in this abstract. An algorithm for searching for inverse elements is found. Let's consider $R_{p,q} (C_{p,q})$ as real (complex) Clifford algebra of dimension m = 2${}^{n}$ (n=p+q) with the basis of $e_{\alpha } =e_{i_{1} } ,...,e_{i_{k}}, 1\le i_{1} <...< i_{k} \le n$, where multiindex $\alpha =i_{1} ...i_{k}$ runs through all subsets in the set $\{ 1,2,...,n\} $, and combination of them is denoted as $\Gamma _{n}.$ Let $e_{0} =1$ be the algebra unit and $e_{1} ,e_{2} ,...,e_{n}$ -- generic basis. Arbitrary element $w$ of Clifford algebra $R_{p,q} (C_{p,q} )$ is written as $w=\sum _{\alpha \in \Gamma _{n} }u_{\alpha } e_{\alpha }, $ where $u_{\alpha }$ are real numbers for the algebra R${}_{p}$${}_{,}$${}_{q}$ and complex numbers for the algebra $C_{p,q}$, where $e_{\alpha } =e_{i_{1} } ,...,e_{i_{k} }, 1\le i_{1} <...< i_{k} \le n.$ Let element $w\in R_{p,q} ,p+q=n$, be reversible. Let's represent it via $w=w_{0} e_{0} +w_{1} e_{n} =w_{0} e_{0} +e_{n} w_{1}^{*}$, where the coefficients belong to an algebra of lower dimension. Special case. If the elements $w_{0}$ and $w_{1}$ are irreversible, then we multiply $w$ by $\hat{w}$ that will be called conjugate, where $\hat{w}=\sum _{\alpha \in \Gamma _{n} }\varepsilon _{\alpha } x_{\alpha } e_{\alpha }$. So, we get element $v=w\hat{w}=\nu _{0} e_{0} +v_{1} e_{n},$ whose elements $v_{0} ,v_{1} $ are reversible. Firstly, this is followed from the corresponding matrix representations of $w$ and $\hat{w}$. Secondly, if we multiply the matrix by the transposed one, we shall get a matrix whose minors are symmetrically located relative to the main diagonal and are not equals to zero. In this case, the transposed matrix corresponds to the conjugate element of the algebra. So, $w^{-1} = \nu ^{-1}\cdot\hat{w},$ where $\nu ^{-1} =(e_{0} -\varepsilon _{n} \nu _{0}^{-1} \nu _{1} \nu _{0}^{*} {}^{-1} \nu _{1}^{*} )^{-1} (e_{0} -\nu _{0}^{-1} \nu _{1} e_{n} )\nu _{0}^{-1} .$ Matrix representations of Clifford algebras and the Schur formula for the determinant of a block matrix are used for proof of elements' reversibility in this formula. Similarly, inverse elements in Clifford algebras over real fields are found. In the case of algebras over the field of complex numbers, instead of the transposed matrix, it is Hermitian-transposed. The same method could be used for algebras over some commutative rings. In particular, isomorphic ones to the center of Clifford algebra. The formula for the inverse element in Grassmann algebra is found.