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# Fill in the blanks in each of the

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

Answer :

The null matrix is the one in which all elements are zero.

If we want to make A = a null matrix we need to multiply it by 0.

0A =

The product of any matrix by the scalar 0 is the null matrix.

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If then the value of x + y is

Mathematics - ExemplarSolve for x and y:

Mathematics - Exemplar

Which of the following statements are True or False

If A and B are two square matrices of the same order, then AB = BA.

Mathematics - ExemplarIf AB = BA for any two square matrices, prove by mathematical induction that (AB)^{n} = A^{n} B^{n}.

If and , then verify (BA)^{2} ≠ B^{2}A^{2}.

Compute the following sums:

RD Sharma - Volume 1

Total number of possible matrices of order 3 × 3 with each entry 2 or 0 is

Mathematics - ExemplarThe matrix is a

Mathematics - ExemplarShow by an example that for A ≠ O, B ≠ O, AB = O.

Mathematics - ExemplarIf , and , verify:

(i) (AB) C = A (BC)

(ii) A(B + C) = AB + AC

Mathematics - Exemplar