Invertible Two by Two Mod 11

Work with arithmetic modulo the prime 11, so every entry is one of the 11 residues {0,1,…,10}{0,1,\dots,10} and every non-zero residue has a multiplicative inverse. Consider the 114=1464111^4 = 14641 matrices

M=[abcd],a,b,c,d∈{0,1,…,10}M = \begin{bmatrix} a & b \ c & d \end{bmatrix}, \qquad a,b,c,d \in {0,1,\dots,10}

MM is invertible exactly when ad−bc≠0(mod11)ad - bc \neq 0 \pmod{11}.

How many of the 14641 matrices are invertible? Answer format: enter an integer.