Find the inverse of the matrix A, if it exists Show A=-407 030

Let A be an nn matrix in which the entries of each row sum to zero. Find |A|.

If A and B are matrices and AB=0, msut |A|=0 or |B|=0? Explain.

Can a matrix with an entire column of zeros have an inverse? Explain why or why not.

Can you explain whether a 2×2 matrix with an entire row of zeros can have an inverse?

Solve for x,y,z and w in the matrix equation wxyx=-432-1+2ywzx.

Solve for x,y and z in the matrix equation 4xyz-1=2yz-x1+24x5-x.

Can a matrix with zeros on the diagonal have an inverse? If so, find an example. If not, prove why not. For simplicity, assume a 22 matrix.

Evaluate the determinant |322214103| , by expanding by minors along the first row.

Determine if the statement is true or false. If the statement is false, then correct it and make it true. For the product of two matrices to be defined, the number of rows of the first matrix must equal the number of columns of the second matrix.