No, a matrix cannot have more than one inverse.

  An inverse of a matrix A is defined as another matrix B, such that the product of A and B gives the identity matrix. In other words, A * B = B * A = I, where I represents the identity matrix.

  If a matrix A has an inverse B, then B is unique. This means that there cannot be more than one matrix B that satisfies the condition A * B = B * A = I.

  To understand why, let's assume that there are two matrices B1 and B2 that both serve as inverses for A.

  Now, if we multiply our assumption by A on the right side, we get:

  A * B1 = A * B2

  Multiplying both sides by the inverse of A:

  (A * B1) * A^-1 = (A * B2) * A^-1

  Using the associative property of matrix multiplication:

  A * (B1 * A^-1) = A * (B2 * A^-1)

  Cancelling the A from both sides:

  B1 * A^-1 = B2 * A^-1

  Now, multiplying both sides by the inverse of A^-1:

  (B1 * A^-1) * (A^-1)^-1 = (B2 * A^-1) * (A^-1)^-1

  Using the property (AB)^-1 = B^-1 * A^-1 :

  B1 * (A^-1 * A)^-1 = B2 * (A^-1 * A)^-1

  Since A * A^-1 = I :

  B1 * I^-1 = B2 * I^-1

  Again, using the property A * I = A:

  B1 = B2

  Therefore, we can conclude that if a matrix A has an inverse, it is unique and there cannot be more than one inverse for a given matrix.