The product of any matrix by the scalar ……. Is the null matrix .

Give an example of a matrix which is a scalar matrix which is not a unit matrix.

Fill in the blanks: If a matrix A is multiplied by the scalar, 0, then we obtain a ……….. Matrix.

True or False statements : If A is any matrix, then AA' is always a symmetric matrix.

If A is any square matrix, then

If the product of two matries is a zero matrix, it is not necessary that one of the matrices is a zero matrix.

If A and B are two mxxn matrices and O is the null matrix of the type mxxn , then show that: A +B = 0 rArr A = -B and B = -A

Let A and b are two square idempotent matrices such that ABpm BA is a null matrix, the value of det (A - B) cann vbe equal

If A is a symmetric matrix , then A^(3) is a …… matrix .

Let A = [a_(ij)] " be a " 3 xx3 matrix and let A_(1) denote the matrix of the cofactors of elements of matrix A and A_(2) be the matrix of cofactors of elements of matrix A_(1) and so on. If A_(n) denote the matrix of cofactros of elements of matrix A_(n -1) , then |A_(n)| equals