MULTIPLYING MATRICES PRACTICE QUESTIONS WORKSHEET

(1)  Find the order of the product matrix AB if

Solution

(2)  If A is of order p x q and B is of order q x r what is the order of AB and BA?        Solution

(3)  A has ‘a’ rows and ‘a + 3 ’ columns. B has ‘b’ rows and ‘17–b’ columns, and if both products AB and BA exist, find a, b?        Solution

(4)  If 

find AB, BA and check if AB = BA?                 Solution

(5)  Given that

verify that A(B + C) = AB + AC .           Solution

(6)  Show that the matrices

satisfy commutative property AB = BA         Solution

(7)  

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

(ii) (A−B)C = AC −BC (iii) (A−B)^T = A^T −B^T          Solution

(8)  If

then show that A² +B² = I .              Solution

(9)  If A = 

prove that AA^T = I .               Solution

(10)  Verify that A² = I when

Solution

(11) 

Solution

(12)  

verify that (AB)^T = B^TA^T         Solution

(13)  

show that A² - 5A + 7I₂  =  0         Solution

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