Show that -a is the inverse of a for the addition opertion '+' on R and `1/a` is the inverse of `a ne 0` for the multiplication opertion 'x' on R.

Find the multiplicative inverse of 2-3i.

Find the multiplicative inverse of 2-3i.

Show that subtraction and division are not binary opertions on N.

Show that the number of binary opertions on {1,2} having 1 as identity and having 2 as the inverse of 2 is exactly one.

Given a non-empty set X, consider the binary opertion **: P(X) xx P (Y) to P (X) given by A **B= A nnB AA A, B in P (X), where P(X) is the power set of X. Show that X is the identity element for this opertion and X is the only invertible elemtn in P(X) with respect to the opertion **.

If A^(2)-A+I=0 then the inverse of the matrix A is

The inverse function of log_e x is

Find the inverse of f(x)={(x ,, x 4):}

If the inverse of implication p to q is defined as ~ p to ~q , then the inverse of the proposition ( p ^^ ~ q) to r is