Question 1 :
If
then find AB and BA. Are they equal ?
Question 2 :
If
verify (AB)C = A(BC).
Question 3 :
If
verify that (AB)^{T} = B^{T}A^{T }
Question 4 :
Prove that
are inverse to each other under matrix multiplication.
Question 5 :
If
find (A + B)C and AC + BC. Is (A + B)C = AC + BC ?
Question 6 :
If A and B are square matrices such that
AB = I and BA = I
then B is
(A) Unit matrix
(B) Null matrix
(C) Multiplicative inverse matrix of A
(D) -A
Question 1 :
If
then find AB and BA. Are they equal ?
Solution :
AB and BA are not equal.
Question 2 :
If
verify (AB)C = A(BC).
Solution :
Associative property is true in matrix multiplication.
Question 3 :
If
verify that (AB)^{T} = B^{T}A^{T }
Question 4 :
Prove that
are inverse to each other under matrix multiplication.
Solution :
If A is a square matrix of order n, and if there exists a square matrix B of the same order n, such that
AB = BA = I
where I is the unit matrix of order n, then B is called the multiplicative inverse matrix of A.
Question 5 :
If
find (A + B)C and AC + BC. Is (A + B)C = AC + BC ?
Solution :
L.H.S :
Add matrices A and B, then multiply (A + B) by C.
R.H.S :
Multiply the matrices A and C. Multiply the matrices B and C.
Add the matrices AC and BC.
So, (A + B)C and AC + BC are equal.
Question 6 :
If A and B are square matrices such that
AB = I and BA = I
then B is
(A) Unit matrix
(B) Null matrix
(C) Multiplicative inverse matrix of A
(D) -A
Solution :
If A is a square matrix of order n, and if there exists a square matrix B of the same order n, such that
AB = BA = I
Then,
Matrices A and B are inverse to each other.
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