MATHS True False[1 Marks ]

True.Solution:
Matrix addition is associative as well as commutative i.e.,
(A + B) + C = A + (B + C) and A + B = B + A, where A, B and C are matrices of same order.

False.Solution:
We can obtain the transpose of a matrix by interchanging the rows and columns.

False.Solution:
For two square matrices of same order it is not always true that AB = BA.

False.Solution:
The necessary condition for addition of two matrices is that both the matrices are of the same order.

False.Solution:
An identity matrix is a square matrix in which all the elements of the principal diagonal are ones and all other elements are zeros.

True.Solution:
Since, matrix addition is commutative ie, A + B = B + A, where A and B are two square matrices.

False.Solution:
If two matrices have same number of rows and same number of columns, we cannot say two matrices are equal as their corresponding elements may be different.

True.Solution:
Two matrices of same order can be subtracted.

True.Solution:
Let A is of order m × n and B is of order p × q.
Therefore, the order of A’ and B’ will be given by n × m and q × p respectively.
Now, we know that, AB will be defined if and only if n = p.
The order of AB will be given by m × q.
Again, B'' will be defined if and only if p = n.
The order of B'A' will be given by q × m.
Hence, if (AB)' = B'A', where A and B are not square matrices, then number of rows in A is equal to number of columns in B and number of columns in A is equal to number of rows in B.

False.Solution:
If AB is defined, it is not necessary that BA is defined.
Also if AB and BA are defined, it not necessary that they have same order. Further if AB and BA are defined and have same order, it is not necessary their corresponding elements are equal.
So, in general AB^BA

False.Solution:
Since, for two non-zero matrices A and B of same order, it can be possible that A.B = 0 = null matrix.

False.Solution:
A matrix is an ordered rectangular array of numbers of function.