NCERT Exemplar Solutions
Class 12 - Mathematics - Chapter 3: Matrices

Fill in the Blanks

_____ matrix is both symmetric and skew symmetric matrix.

Sum of two skew symmetric matrices is always _____ matrix.

The negative of a matrix is obtained by multiplying it by _____.

The product of any matrix by the scalar _____ is the null matrix.

A matrix which is not a square matrix is called a _____ matrix.

Matrix multiplication is _____ over addition.

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

If A is a skew symmetric matrix, then A\(^2\) is a ____.

If A is skew symmetric, then kA is a _____ (k is any scalar).

If A is symmetric matrix, then B'AB is ____.

If A and B are symmetric matrices of same order, then AB is symmetric if and only if ____.

In applying one or more row operations while finding A\(^{-1}\) by elementary row operations, we obtain all zeros in one or more, then A\(^{-1}\) ____.

If A and B are square matrices of the same order, then (i) (AB)' = ____.

(ii) (kA)' = ____ (k is any scalar)

(iii) [k(A − B)]' = ____.

If A and B are symmetric matrices, then (i) AB − BA is a ____.

(ii) BA − 2AB is a ____.