Show that every square matrix `A` can be uniquely expressed as `P+i Q ,w h e r ePa n dQ` are Hermitian matrices.

Prove that every square matrix can be uniquely expressed as the sum of a symmetric matrix and a skew-symmetric matrix.

Consider the following statements. I. The inverse of a square matrix, if it exists, is unique. II. If A and B are singular matrices of order n, then AB is also a singular matrix of order n. Which of the statements given above is/are correct ?

Let A be a square matrix such that each element of a row/column of A is expressed as the sum of two or more terms.Then; the determinant of A can be expressed as the sum of the determinants of two or more matrices of the same order.

Consider the following statements. I. The inverse of the square matrix, if it exits, is unique. II. If A and B are singular matrices of order n. then AB is also a singular matrix of order n. Which of the statements given above is/are correct ?

If A is a non zero square matrix of order n with det(I+A)!=0 and A^(3)=0, where I,O are unit and null matrices of order n xx n respectively then (I+A)^(-1)=

Show that 2.bar(37) can be express in the form of (p)/(q).

Show that 1.272727=1.27 can be expressed in the form (p)/(q), where p and q are integers and q!=0