alleryRegroup the product (AB)C without reordering its three 2×2 factors.
- A(CB)
- C(AB)
- (BA)C
- A(BC)
Show answer and solution
Correct answer: D. A(BC)
Matrix multiplication is associative, so regrouping without reordering preserves the product.
ICSE Class 10 Algebra: Equations, Inequations & Matrices — practice questions — page 5
Explore 212 free Algebra: Equations, Inequations & Matrices questions in ICSE Class 10 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 121–150 of 212.
Regroup the product (AB)C without reordering its three 2×2 factors.Read the answer and worked solution →Choose the correct expansion when A multiplies B+C on the left.Read the answer and worked solution →A=[[1,x],[0,2]], B=[[2,3],[0,1]]. If AB=BA, find x.Read the answer and worked solution →A=[[2,x],[0,1]], B=[[1,3],[2,4]]. If AB has top-right entry 0, find x.Read the answer and worked solution →A=[[x,0],[0,-1]]. For which real x is A² the identity matrix?Read the answer and worked solution →A=[[x,1],[0,y]], B=[[1,2],[3,1]]. AB has first column [5,9]. Find x+y.Read the answer and worked solution →Scaling A by rational k changes the product AB to which expression?Read the answer and worked solution →A+B=[[8,4],[2,6]] and A-B=[[2,0],[-4,2]]. Find A's bottom-left entry.Read the answer and worked solution →A=[[1,-2],[3,0]], B=[[-1,1],[2,-4]]. Evaluate (2A-B)₁₂.Read the answer and worked solution →Stock=[[12,8],[7,9]] has rows Monday, Tuesday and columns pens, books. What does 7 represent?Read the answer and worked solution →Quantities Q: buyer rows, item columns. Prices P: item rows, shop columns. What does (QP)₂₁ give?Read the answer and worked solution →Two days' sales are [[3,2],[1,4]] and [[2,1],[0,3]], with matching labels. What are total sales?Read the answer and worked solution →Q=[[2,3],[1,4]], P=[[4,5],[10,8]]. Which is the smaller entry in row 1 of QP?Read the answer and worked solution →3A-2B=I, where I is the 2×2 identity and B=[[1,2],[0,1]]. Find A's top-right entry.Read the answer and worked solution →In the proportion a:b=c:d, which terms are the means?Read the answer and worked solution →For positive a,b,c,d, a:b=c:d is equivalent toRead the answer and worked solution →For positive terms, alternendo changes a:b=c:d intoRead the answer and worked solution →With positive a,b,c,d and a:b=c:d, dividendo givesRead the answer and worked solution →If positive a:b=c:d, what must equal (a+b):a?Read the answer and worked solution →For positive a:b=c:d, alternendo followed by invertendo yieldsRead the answer and worked solution →If a>b>0 and a:b=c:d with c,d>0, which need NOT hold?Read the answer and worked solution →When a=b≠0, which ratio is undefined?Read the answer and worked solution →Given positive a:b=3:2, calculate (2a+3b):(3a−b).Read the answer and worked solution →For positive a:b=2:1, evaluate (a²+b²):(a²−b²).Read the answer and worked solution →If a>b>0 and (a+b):(a−b)=7:3, determine a:b.Read the answer and worked solution →Solve (x+2):(x−1)=4:3, where x>1.Read the answer and worked solution →For x>1, (√x+1):(√x−1)=3:1. Find x.Read the answer and worked solution →With x≠1,2, solve (x+1)/(x−1)=(x+2)/(x−2).Read the answer and worked solution →Positive a/b=c/d=2/3. Find (2a+3c)/(2b+3d).Read the answer and worked solution →Two positive numbers are in ratio 3:5. Adding 6 to each makes the ratio 2:3. Smaller original number?Read the answer and worked solution →
Worked practice questions
Choose the correct expansion when A multiplies B+C on the left.
- AB+CA
- BA+AC
- AB+AC
- BA+CA
Show answer and solution
Correct answer: C. AB+AC
Left multiplication distributes as AB+AC while preserving the order of the factors.
A=[[1,x],[0,2]], B=[[2,3],[0,1]]. If AB=BA, find x.
- -1
- -3
- 3
- 1
Show answer and solution
Correct answer: B. -3
Matching the top-right entries gives 3+x=2x+6, hence x=-3.
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